Shutting down a system by simply "pulling the plug" (like killing the surge protector, etc.) can cause major operating system problems. UNIX/Mac OS X is very picky about how it starts up and shuts down -- critical system processes are done at these times. If a proper shutdown procedure is interrupted or bypassed completely, you can hose your entire system and render it unbootable in one swell foop.
Even though Disk Utility reports no problems with the actual hard drive, there still may be system problems buried deep in the thousands of files that Mac OS X uses.
My first instinct would be to create a new user account and see if the problems persist there -- if not, then it can be safely assumed that a preference file or something associated with the original user account has gone awry. If it doesn't fix the problem, that indicates that the problem probably has something to do more with the underlying system than with a wonky preference file.
If I were in your situation, I would completely wipe the drive clean and reinstall Mac OS X -- this always guarantees a perfect, clean, 110% working system unless you've got some sort of hardware problem. An "Archive & Install" process is basically the same thing, but can carry the problem over to the new install since it reuses some files/settings already present on the drive.
At any rate, keep a good backup of your data -- this should go without saying and should be done regularly, problems or no problems. Try the new user account and see if that helps -- barring that, do an Archive & Install... and, lastly, I would try a clean install. You may also want to check your RAM -- take out any 3rd party modules and see if that helps. You can also run the Hardware Diagnostics CD that Apple provided you with the system to see if you've got some hardware problem.
