As to what happens on the screen when pressign the button: there is nothing at all on the screen, just pitch black.
So memory, another mouse, and all those other 'try this and try that' ideas will not help. Are completely irrelevant to your symptoms. Either get the meter to do what a junior high school science student can do. Or take it to a computer repairman who will do the same thing.
Age of the PC, those part numbers, etc report little that is useful. What is problematic and what the meter will report is essentially same on any Pentium computer (with minor detail differences that are irrelevant here). All you need do is take measurements.30 seconds of labor with zero risks. Then the few who actually have advanced knowledge will reply accordingly.
If you fear using a meter, then you have no business swapping memory or doing other things that are potentially more dangerous. For example, when you removed memory, did you first disconnect the AC plug? If not, you have put hardware at risk. Why? Those meter numbers would make that obvious. Potential hardware damage and other complications is why to probe with a meter long before swapping or shotgunning anything.
If you fear using the meter, you have no business trying something more dangerous to the machine. Take it to the shop. If you want to fix it and learn, get the meter.