IMac 24" OS X 10.5.8 crashes after startup

Question

After startup, my iMac crashes after a short while (from 10 seconds up to 10 minutes). The screen freezes and the keyboard doesn't respond. I can't click, however, i can move the cursor around. This iMac was bought 2008 and I've never had any problems like this before, and I have no idea what made it behave this way. (I noticed it had crashed when I tried to wake it up from sleep mode a couple of days ago.)
Things I tried that didn't fix the problem:
1. Shutting down and disconnecting power cord for 30 seconds
2. Reseting PRAM
3. Created a new login-account
4. Repaired disc permissions in Disc Utilities
5. Hardware test (holding "d" during startup)
(OBS. I've tried the extended hardware test several times but sooner or later it crashes, always before the test is finished!)
In Safe Mode (holding "shift" during startup) though, it doesn't crash, but then I can't have sound etc.
What kind of problem could this be? What should I do?

Answer 1

You mentioned running Apple Hardware Test however I'm guessing you may not have run in Extended Mode. If you did not then you really haven't tested it. When you start AHT look for Extended Mode and follow the instructions. This test will take significantly longer to do. My guess is  you have  temp sensor or HD problem.
Another thing you can do is run Activity Monitor when operating normally and look to see if you have any processes that are using a lot of %CPU, if you do that's a sign you have a problem process. You can also look for how much FREE RAM you have (it's under the System Memory tab) however being low on RAM would not cause a crash it would cause a slowdown.