Grey Screen Apple logo No spinner

I have a 24" iMac 3.06 Core 2 Duo. When I try to start it, it gets stuck at the grey screen with the apple logo. The spinner is stuck and not spinning.

This computer has always had some issues. I'm wondering if it might be a hard drive cable. I had read something awhile back with similar symptoms but never followed up.

The computer came with 10.5 on it and I had upgraded to 10.6. when it came out. Sometime during 2009 the hard drive went bad, replaced under applecare..

My computer has always had a problem sleeping. You put it to sleep and it immediately wakes up. Apple said it was probably a network issue. Sometimes you can make it sleep, sometimes it wouldn't.

Any time I try to boot from a DVD, of ANY version it will just go to a blank grey screen.. DVD spins up and back down, eventually spits out.

When 10.7 came out, I could not get the computer to boot from it.

I took it in to Apple and they got it 10.7 installed..

10.7 slowed the computer down badly.

When 10.8 came out, I tried installing that, but again, just got the grey screen. I ended up getting 10.6.8 reinstalled, can't remember how, but left it there because of speed issue. 10.6.8 ran really well.

So, now I can't log in. I have a full time machine backup. I am willing to swap hard drives, but I think that something more is the issue. DVDs would load fine, but just wouldn't boot from it..

Could this be a bad cable/cables for hard drive and or DVD?