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Here is a check-list for some basic, unspecific trouble-shooting.
1. Restart the computer
2. Deactivate/Uninstall system haxies and third-party extensions (e.g. ASM, Norton AntiVirus, etc.)
3. Check/fix the filesystem as outlined in this article: Using Disk Utility and fsck for file system maintenance in Mac OS X and Using Disk Utility in Mac OS X 10.4.3 or later to verify or repair disks
4. Check for at least 5 GB of free space on the boot volume. Mac OS X needs at least that amount in order to run properly.
5. Repair permissions: Go to Applications > Utilities > Disk Utility, choose your HD in the sidebar and click "Repair Permissions"
6. If one specific application gives you a headache, move it's preference-file to the desktop (User/Library/Preferences or in case of system "programs"
in Library/Preferences). If this solves the problem you may trash it.
7. Create a new user account, and see if the problem persists.
8. Clear system & user caches with either Tiger Cache Cleaner or Cocktail.
9. Unplug all USB- and Firewire devices except original Apple mouse and keyboard.
10. Startup in Safe-mode and see if the problem persists: Starting up in Safe Mode
11. Repair and replace the directory with DiskWarrior or TechTool Pro 4
12. Zap PRAM: How to Reset PRAM and NVRAM
13. Unplug 3rd Party PCI cards.
14. Reinstall the latest combo updater.
15. Check the hard drive for bad blocks (e.g. with Drive 10 or TechTool Pro 4).
16. Take out 3rd party RAM.
17. Run the Apple hardware diagnostic CD.
18. Reset PMU: Resetting Power Management Unit (PMU), Power Mac G4 (AGP Graphics/Gigabit Ethernet): Resetting the PMU on the Logic Board, Resetting PowerBook and iBook Power Management Unit (PMU)
19. Reinstall the system from scratch ( Installation options and their meaning )
20. Send the machine back to Apple.
Special situation: Macromedia products do not launch: Some Macromedia applications won't run after upgrading to Macintosh OS X version 10.2.8 or to Panther (version 10.3)
For further reference you might also want to read these articles:
OS X Routine Maintenance and Generic Troubleshooting
Mac OS X 10.3/10.4: System maintenance
Isolating issues in Mac OS X
Mac OS X 10.3.3: USB device, FireWire device, RAID card or SCSI card doesn't work after updating to 10.3.3
Your Mac won't start up in Mac OS X
Mac OS X: What Is a Kernel Panic?
Mac OS X: How to Log a Kernel Panic
Mac OS X: If Your Computer Stops Responding, "Hangs", or "Freezes"
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