My iMac keeps freezing. Help please?

This is a hardware error, and I'm afraid you need to take it in for repair.

It probably means a new logic board. (But get it diagnosed anyway; you never know.) Not a cheap repair. Maybe worth something for someone to cannibalize for parts. I'd start saving pennies. Even a "new" (means refurbed) logic board will probably break down in record time. Sorry 😟

Save your pennies! Then you'll have a lovely new computer, and if you get Apple Care, three years of service as well. BTW, Apple have some pretty good deals on refurbished machine, with the same warranties.

As it happened, on the iMac I was working on, which I believe is identical to yours, the video ram test ran abnormally slow, although there were no errors. It was suggested to me that I clean the optical drive and try the AHT again.

This may be a long shot and grasping at straws, but probably worth a try. Especially if the machine seems to be working properly now. I'm thinking the accuracy of the AHT could be affected if the optical drive is not functioning properly. I'm thinking that if you really do have a video RAM problem, there would be symptoms of some sort, although I personally don't know what to look for. Maybe someone else on this thread would know.

Probably prudent to see if you can continue to use your iMac as is as long as possible and not put any money into paying someone to repair it. Consider running it from an external FireWire drive if the internal drive dies--external FW drives are useful all by themselves, so that would not be money wasted. Just keep a good up to date backup at all times until you are able to get a handle on what's actually wrong with the machine and what it would actually take to fix it.

Also, check out the ifixit site and consider working on the iMac yourself. Also check on Craig's list and EBay to see what machines like yours are actually selling for. Or what parts are selling for. That will give you a good handle on what your machine is worth in today's market so that you don't end up spending more than it's worth to fix it. Bear in mind any machine with a known problem will sell for less than one in good shape.

Did you ever download and run SMART Utility? If not, do so. I still think your fundamental problem is a failing hard drive, even if Disk Utility doesn't think so.

Good luck!