486 don't need much cooling. The challenge is finding a way to attach the cooler to the processor 😀

I've got one that has clips and a fan on it. Works well. On a test bench I do the same, just place a Socket 7 cooler ontop.

Faulty cache should give you errors pretty much straight away. Check if the jumpers are configured correctly. It's worth removing them all, checking the legs, and putting them back in carefully. That can sometimes fix a loose connection.

Whenever external cache is enabled the PC hangs during boot (it goes through POST just fine). I also triple-checked the jumper settings, and the cache is detected correctly (256kb cache). I think I'll have to buy a proper tool to remove the ICs, as they do not want to come off easily and I'd rather not use a screwdriver for this if I have to put too much force.