Computer won't stay on

Hello! I want to preface this by saying that I am very much a newbie, and will probably use wrong terms for stuff, but I'm trying my best to learn.

Several years ago a friend (who I have fallen out of contact since), built me a pc from his old pc when he built himself a new one. So I am aware every part is old and it's a miracle it has actually worked this long.

Few weeks ago it suddenly shut off and and since then I haven't managed to get it stay on past login screen. There was quite a lot of dust inside, and I hoped that was the culprit, but I have cleaned it to best of my ability and no dice. Although the short time the computer is on it sounds a lot better (surprising, I know...)

Next I figured overheating might be an issue, but according the little screen on the casing, it doesn't go above 21°C before shutting off, so I don't think it's that either?

I'm at loss on what to try next.

I'm prepared to possibility of having to replace parts, but because I'm on low income with no savings, it would need to be one or two parts at the time, so I'd prefer to have better idea what's wrong first.

Thank you in advance!