Has anybody ever founds someone with AIDS who did not have HIV?

According to skeptics, yes, in all but name. The standard skeptical argument is that AIDS, as it is currently defined, includes HIV+ as a necessary diagnostic criterion, and that this is a circular definition: if someone presents with all the symptoms of AIDS, but tests HIV-, then they are defined to not have AIDS. This means that 100% of diagnosed AIDS patients will be HIV+, just by definition, not due to a meaningful correlation.

It would seem to require only a microscope, as syringe and a sufficient sample of people with AIDS

The skeptical position here is that you can't actually see a virus with an optical microscope (which I believe is true), and "HIV tests" are actually just testing for HIV antibodies (or substances alleged to be HIV antibodies), not HIV itself.

I'm not endorsing these positions, just passing them along, btw.