What part of the computer has gold

Most electronics have gold. Although they used very very sparingly.

For example on a CPU - the contacts have some gold.

Some traces on the motherboard have gold.

Toms did an article on how to extract gold from computers - but the cost of the materials needed to extract the gold, as well as the dangerousness of the materials being used made it not worthwhile.

I wouldn't bother doing it. You could possibly shorten your lifespan literally if done incorrectly.