SiSoft SANDRA and Everest have benchmarking but not true diagnostics as such.

My advice would be to talk to AMD and Intel and let them dissuade you.

What has happened is a very rare occurrence. Normally a CPU either works or it does not. To have one produce errors in displaying images only, and then only distortion is exceptionally rare, with a probability less than 1 in 100,000.

It isn't worth the expense or effort.

You should have found the problem using traditional methods. I guess someone decided to cut their losses and "blamed the motherboard" they obviously did not try another processor.

A processor diagnostics tool is very expensive and would require removing the processor anyway, so putting in a known good one would be easier, quicker and a lot cheaper!

I have quite a collection of old components that I use for diagnostics purposes

I would suggest that your workplace looks at developing diagnostics checklists. You can then price the maximum time that might be required, for given symptoms. The customer would then have to agree to this up front.

Cheers