Odd collection of problems with newly purchased used iMac

I have recently purchased a used iMac from eBay (an Intel model from 2006). I've been trying to get it set up over the last couple of days and have had one problem after another. I suspect a hardware problem, but would like to be able to pin it down before I contact the seller and ask them to take (and pay for shipping on) a return.

Here are the symptoms:

The iMac came with OS 10.5 freshly installed. I ran Software Update, which offered to install a combo update to bring it up to 10.5.8. I said yes, and it downloaded the update, restarted to complete the installation, and then hung at the same point for hours during the installation. I finally gave up and shutdown by holding down the power button, then restarted and tried again to run the update through Software Update -- and it hung again. I did a new fresh install of 10.5, and thereafter was able to download and install the update properly.

Afterward, I used the computer for a while without a problem and installed a few applications that I have known to be compatible with both Leopard and Intel Macs in the past. After it finished with the installing, I opened a Safari window and the computer became unresponsive, except that I could move the spinning beach ball around the screen. I left it for ten or fifteen minutes, then tried to force quit, but the force quit dialog box wouldn't come up. I held down the power button to shut down, waited ten seconds, and restarted.

Suspecting bad memory, I installed Applejack and Memtest and used Applejack to run Memtest in single user mode. It found no problems with the memory. (The computer did not come with a disk to check the hardware.)

I restarted, tried to open Safari and found that the cursor was "stuck." I went to check the USB connection for the mouse, when I heard the startup chime and then watched as the iMac rebooted on its own. A screen notice said:

The computer was restarted after Mac OS X quit unexpectedly. Click report to see more details or send a report to Apple.

The report read:

_______________

Interval Since Last Panic Report: 17646 sec

Panics Since Last Report: 1

Anonymous UUID: 049895A2-15D4-4AB9-B189-349747A8704F

Thu Oct 25 16:23:35 2012

Machine-check capabilities (cpu 1) 0x0000000000000006:

family: 6 model: 14 stepping: 8 microcode: 0

Genuine Intel(R) CPU 1500 @ 2.00GHz

6 error-reporting banks

Machine-check status 0x0000000000000005:

restart IP valid

machine-check in progress

MCA error-reporting registers:

IA32_MC0_STATUS(0x401): 0xb200004000000800 valid

MCA error code: 0x0800

Model specific error code: 0x0000

Other information: 0x00000040

Status bits:

Processor context corrupt

Error enabled

Uncorrected error

IA32_MC1_STATUS(0x405): 0x0000000000000000 invalid

IA32_MC2_STATUS(0x409): 0x0000000000000000 invalid

IA32_MC3_STATUS(0x40d): 0x0000000000000000 invalid

IA32_MC4_STATUS(0x411): 0x0000000000000011 invalid

IA32_MC5_STATUS(0x415): 0xb200120020080400 valid

MCA error code: 0x0400

Model specific error code: 0x2008

Other information: 0x00001200

Status bits:

Processor context corrupt

Error enabled

Uncorrected error

panic(cpu 1 caller 0x001AA46A): Machine-check at 0x00c798b2, thread:0x35527d8, code:0x12, registers:

CR0: 0x8001003b, CR2: 0x008ec000, CR3: 0x010e1000, CR4: 0x000006e0

EAX: 0x00000010, EBX: 0x0361c140, ECX: 0x00000001, EDX: 0x00c7f800

ESP: 0x2a8bfc70, EBP: 0x2a8bfc98, ESI: 0x03614084, EDI: 0x00c7ecb0

EFL: 0x00000002, EIP: 0x00c798b2

Backtrace (CPU 1), Frame : Return Address (4 potential args on stack)

0x4f8f18 : 0x12b4c6 (0x45f91c 0x4f8f4c 0x13355c 0x0)

0x4f8f68 : 0x1aa46a (0x4692a4 0xc798b2 0x35527d8 0x12)

0x4f8fe8 : 0x1a2525 (0x12 0x0 0x0 0x0)

Backtrace terminated-invalid frame pointer 0

BSD process name corresponding to current thread: kernel_task

Mac OS version:

9L31a

Kernel version:

Darwin Kernel Version 9.8.0: Wed Jul 15 16:55:01 PDT 2009; root:xnu-1228.15.4~1/RELEASE_I386

System model name: iMac4,1 (Mac-F42787C8)

System uptime in nanoseconds: 373754620262

unloaded kexts:

com.apple.driver.InternalModemSupport 2.4.0 - last unloaded 84297245239

loaded kexts:

com.apple.driver.InternalModemSupport 2.4.0 - last loaded 14244796671

com.apple.filesystems.autofs 2.0.2

com.apple.driver.AppleHDAPlatformDriver 1.7.1a2

com.apple.driver.AppleHWSensor 1.9d0

com.apple.driver.AppleHDAHardwareConfigDriver 1.7.1a2

com.apple.driver.AppleUpstreamUserClient 2.7.5

com.apple.driver.AppleHDA 1.7.1a2

com.apple.kext.ATY_Wormy 5.4.8

com.apple.driver.AppleGraphicsControl 2.8.15

com.apple.iokit.IOBluetoothSerialManager 2.1.9f10

com.apple.ATIRadeonX1000 5.4.8

com.apple.Dont_Steal_Mac_OS_X 6.0.3

com.apple.driver.AppleBacklight 1.6.0

com.apple.driver.AppleHDAController 1.7.1a2

com.apple.driver.AudioIPCDriver 1.0.6

com.apple.driver.AppleIRController 113

com.apple.driver.ACPI_SMC_PlatformPlugin 3.4.0a17

com.apple.driver.AppleLPC 1.3.1

com.apple.driver.AppleTyMCEDriver 1.0.0d28

com.apple.iokit.IOFireWireIP 1.7.7

com.apple.driver.CSRUSBBluetoothHCIController 2.1.9f10

com.apple.driver.AppleUSBHIDMouse 1.2.4b3

com.apple.driver.CSRHIDTransitionDriver 2.1.9f10

com.apple.driver.AppleUSBMergeNub 3.5.2

com.apple.iokit.IOSCSIMultimediaCommandsDevice 2.1.1

com.apple.iokit.SCSITaskUserClient 2.1.1

com.apple.driver.XsanFilter 2.7.91

com.apple.iokit.IOATAPIProtocolTransport 1.5.3

com.apple.driver.AppleFileSystemDriver 1.1.0

com.apple.iokit.IOAHCIBlockStorage 1.2.2

com.apple.driver.AppleUSBHub 3.4.9

com.apple.iokit.IOUSBUserClient 3.5.2

com.apple.driver.AppleFWOHCI 3.9.7

com.apple.driver.AirPortBrcm43xx 367.91.22

com.apple.driver.AppleAHCIPort 1.7.0

com.apple.driver.AppleIntelPIIXATA 2.0.1

com.apple.iokit.AppleYukon2 3.1.13b2

com.apple.driver.AppleUSBEHCI 3.4.6

com.apple.driver.AppleUSBUHCI 3.5.2

com.apple.driver.AppleEFINVRAM 1.2.0

com.apple.driver.AppleRTC 1.2.3

com.apple.driver.AppleHPET 1.4

com.apple.driver.AppleACPIPCI 1.2.5

com.apple.driver.AppleACPIButtons 1.2.5

com.apple.driver.AppleSMBIOS 1.4

com.apple.driver.AppleACPIEC 1.2.5

com.apple.driver.AppleAPIC 1.4

com.apple.security.seatbelt 107.12

com.apple.nke.applicationfirewall 1.8.77

com.apple.security.TMSafetyNet 3

com.apple.driver.AppleIntelCPUPowerManagement 76.2.0

com.apple.driver.DiskImages 199

com.apple.BootCache 30.4

com.apple.driver.DspFuncLib 1.7.1a2

com.apple.iokit.IOSerialFamily 9.4

com.apple.iokit.IONDRVSupport 1.7.3

com.apple.iokit.IOGraphicsFamily 1.7.3

com.apple.iokit.IOHDAFamily 1.7.1a2

com.apple.iokit.IOAudioFamily 1.6.9fc5

com.apple.kext.OSvKernDSPLib 1.1

com.apple.driver.IOPlatformPluginFamily 3.4.0a17

com.apple.driver.AppleSMC 2.3.1d1

com.apple.driver.AppleUSBBluetoothHCIController 2.1.9f10

com.apple.iokit.IOBluetoothFamily 2.1.9f10

com.apple.driver.AppleHIDMouse 1.2.4b3

com.apple.iokit.IOUSBHIDDriver 3.4.6

com.apple.driver.AppleUSBComposite 3.2.0

com.apple.iokit.IOSCSIBlockCommandsDevice 2.1.1

com.apple.iokit.IOBDStorageFamily 1.5

com.apple.iokit.IODVDStorageFamily 1.5

com.apple.iokit.IOCDStorageFamily 1.5

com.apple.iokit.IOSCSIArchitectureModelFamily 2.1.1

com.apple.iokit.IOFireWireFamily 3.4.9

com.apple.iokit.IO80211Family 216.1

com.apple.iokit.IOAHCIFamily 1.5.0

com.apple.iokit.IOATAFamily 2.0.1

com.apple.iokit.IONetworkingFamily 1.6.1

com.apple.iokit.IOUSBFamily 3.5.2

com.apple.driver.AppleEFIRuntime 1.2.0

com.apple.iokit.IOSMBusFamily 1.1

com.apple.iokit.IOStorageFamily 1.5.6

com.apple.iokit.IOHIDFamily 1.5.5

com.apple.driver.AppleACPIPlatform 1.2.5

com.apple.iokit.IOACPIFamily 1.2.0

com.apple.iokit.IOPCIFamily 2.6

___________________

The report also showed an unusual screen artifact -- a black line that went across it, but was not on the rest of the screen.

I opened Safari to look up information about kernel panics, and found a similar black line across its window. Later, on a different page, there was a blue line -- and on another page after that, various blue and black lines appeared. I restarted Safari, and it still showed odd lines. Those lines were only on the Safari window, not across the whole screen.

I have very little experience troubleshooting problems of this sort, and I'm hoping someone with more experience can tell me what significance the panic report has and how it might relate to the other problems. Like I said, I expect that I'll need to return this iMac (which I've only had for a couple of days now), but I'd like to have a clearer idea of what's going on before I contact the seller.

Any help would be much appreciated!