It's probably time to take it into a tech somewhere. Either an Apple store or just look in the phone book for an Apple-repair place.
This really sounds like a hardware problem somewhere. Whether it's the hard drive, the RAM, the motherboard, or something else I can only guess at. I think you'll have to have someone open it up and do some actual tests on the thing.
The ONLY other thing I can think of is that maybe the drive hasn't been properly formatted?
Follow these instructions from the Apple web site and try re-loading OS X one more time before you take it somewhere. (This will erase ALL data on the drive.)
1. Insert the Mac OS X CD.
2. Restart the computer.
3. Immediately after the startup sound, press and hold the "C" key to start up from CD.
4. When the Installer screen appears, do not click Continue. Instead, choose Installer > Open Disk Utilities.
5. Select the hard drive to erase.
6. Click the Erase tab.
7. Select the volume format from the Volume Format pop-up menu. (Mac Extended Journaling On)
8. Click Options.
9. Select the checkbox for "Zero all data".
10. Click OK.
11. Click Erase.