Well you are on the right track thinking it is hardware. The included hardware test is not very good because it just looks for obvious hardware errors. To see if the hard drive is still good you will have to play Unix guru. However it is not that hard. We will have to boot into single user mode and run a test. So follow these tests:
1) Restart the Mac while holding down the Command key (the clover key)+the letter s.
2) Hold the command button+s until a black screen appears with writing on it.
3) At the first chance it gives you a prompt, type these letter: fsck -fy
(Make sure there is a space between fsck and the -fy)
4) Let the test run. It will check throughly your hard disk. Wait a couple of minutes until the test finishes. The output of the test should say all is well. If the output say something is wrong, run the test again (fsck-fy). Sometimes the program can right over or skip over a bad sector on the disk. If the second test still does not fix the problem, you have a bad hard disk.
5) To get out of single user mode just type ate the prompt: reboot
6) The Mac will reboot into normal mode.
Also OS X has a "Safe Mode" you can boot into. The "Safe Mode" will turn off all third party add-ons to see if one of those is messing with the system. To boot into "Safe Mode" just restart holding down the "shift" key. Booting into "safe mode" with tell you if one of your third party applications is to blame for the problems.
Lastly I believe your first idea that it is a hardware problem is right on the money. You just have to find what hardware is messing up. Good Luck.
Mac Pro Dual 2.8 Quad (2nd gen), 14G Ram, Two DVD-RW Drives, OS X 10.8.3
2006 Mac Book Pro 2.16 (first Gen) OS X 10.7.4
2TB Time Capsule, 2 TB
32G iPhone 4S Black, iPad (3rd Gen) 32G Black