Bad Logic Board?

I own a 20" Mid 2007 2.4GHZ IMac that over the last 3 or 4 months have been giving me problems such as shutting down from time to time and starting right back up. Most of the time I found this doing it if you hit the desk with your knee or something similar. I took it to the Apple Guru's and they told me the logic board, hard drive, optical drive all need to be replaced. I didn't fix it as they wanted 800+ to repair. I took it home and it worked ok for a while and started doing it again, now it wont turn on at all? Any suggestions? I took it apart and looks like Apple never even opened it as it looked un touched. Capacitors look fine but I LCD Heat Cable was pinched pretty hard next to the fan could this cause this problem? I am also thinking of having the board repaired than replaced as most things i've read they say to repair the one you have. Any thoughts?

Theses machines have heat sensors on the cpu...if they go bad the machine shuts down.
Just a thought.