Try the standard suite of diagnostics-first a PMU and PRAM reset.
If this doesn't get you anywhere, you may have a corrupt OS install. Try booting into Singe User Mode(command+S) then type /sbin/fsck -fy when the command prompt appears. This will take a few minutes but will either say "The Disk appears OK" or "FILE SYSTEM WAS MODIFIED." Keep running fsck until it no longer returns the "file system was modified" message.
If this doesn't do anything, boot off an OS X install disk(same version as what you're running) or boot the computer in target disk mode(hold down T) and connect it via a Firewire cable to another computer running the same version of OS X. In either case, use Disk Utility to repair permissions on the drive.
If this still fails, try an archive and install on OS X.