MacBookPro3,1 runs well with 10.6.8 but can't install Mavericks or Mountain Lion

I have an old "Santa Rosa" MBP from August 2007. It runs 10.6.8 perfectively well but I thought I'd install Mavericks to see what the future is like. Unfortunately it failed midway through the install with a "hardware issue" message and a request for reboot. Fortunately it hadn't changed the OS on the hard disk so all I had to do was go into Startup Manager and boot the old installation.

I then tried to install Mountain Lion onto a USB drive and it gave the same hardware/reboot message. Curiously I can safe-boot into Mountain Lion.

I ran the Apple hardware tests and everything passes. The top of the kernel panic file in /USB/Library/Logs/DiagnosticReports/ reads:

Interval Since Last Panic Report: 1097 sec

Panics Since Last Report: 1

Anonymous UUID: C1ED3F67-A747-6CE7-96A7-E79CDE3F77A8

Tue Dec 10 08:15:34 2013

panic(cpu 0 caller 0xffffff7f85f55281): NVRM[0/1:0:0]: Read Error 0x00002500: CFG 0xffffffff 0xffffffff 0xffffffff, BAR0 0xd2000000 0xffffff80833d2000 0x084700a2, D0, P2/4

Backtrace (CPU 0), Frame : Return Address

....

Kernel Extensions in backtrace:

com.apple.NVDAResman(8.1.6)[EA4F9902-5AAE-3F1D-A846-3796221C8C91]@0xffffff7f85e f4000->0xffffff7f86195fff

dependency: com.apple.iokit.IOPCIFamily(2.8)[6C1D646D-7E5E-3D7F-A557-2CBA398FF878]@0xffffff 7f84c51000

dependency: com.apple.iokit.IONDRVSupport(2.3.7)[F16E015E-1ABE-3C40-AC71-BC54F4BE442E]@0xff ffff7f85cc4000

dependency: com.apple.iokit.IOGraphicsFamily(2.3.7)[9928306E-3508-3DBC-80A4-D8F1D87650D7]@0 xffffff7f85a67000

com.apple.nvidia.nv50hal(8.1.6)[3455BCFE-565A-3FE5-9F0B-855BCB6CC9B3]@0xffffff7 f86196000->0xffffff7f86469fff

dependency: com.apple.NVDAResman(8.1.6)[EA4F9902-5AAE-3F1D-A846-3796221C8C91]@0xffffff7f85e f4000

dependency: com.apple.iokit.IOPCIFamily(2.8)[6C1D646D-7E5E-3D7F-A557-2CBA398FF878]@0xffffff 7f84c51000

...

One complication with the machine is that it had the NVIDIA cracked soldering problem. A year ago I sent the motherboard to a shop in California that put on a new graphics chip and it's run well since then although it reports 128MB of video RAM instead of the standard 256MB.

This model is supposed to run everything up through Mavericks. Is there anything obvious I've missed?