Has to be a hardware problem, then. Sorry.
You may want to try running the Apple Hardware Test - nothing like the techs have at the Apple Store or an AASP, but it may tell you something. Even if you don't get any errors, I think that it's time to take the machine to your local Apple Store (or an AASP) and have them diagnose the problem. Doesn't sound as if it's a problem with your hard drive and it may be something as simple as your SATA cable - but only the techies with their diagnostics will be able to tell.
Sorry that it's been such a grueling process with no 'fix' - we tried.