Hey, Greg,
I'd try what Sonicus suggested. You can grab an external HD case with a USB connector and see if your iMac recognizes that. But definitely first try a different cable. It does sound mechanical- maybe it overheated due to a failure of the cooling system...
If you can get the HD out, you should be able to pop it into an External enclosure (very cheap- I got mine on eBay for under $20, I believe). What you should definitely do is grab an extra HD, or another external HD, and get a program called Super Duper. You can find that at:
www.shirtpocket.com You can easily clone that HD, thus making a true copy of it which is also bootable. I've used this several times with great success. It's very simple- but definitely read the directions- the main thing you have to keep in mind is to format the new blank HD as Mac Journaled I believe- don't quote me on that, but I'm pretty sure.
If you do this, you will have a carbon copy of your HD with all of your files intact and exactly as they currently appear.
Good Luck!!!
Frank