Desktop HP Computer power problem

Hi, ALL,
I have a very weird power problem, that I can't sort out...

I have an old HP desktop with Linux. It worked fine until 2 days ago, when it suddenly shuts off.
I unplugged power cable, left it overnight and next morning when I plugged it in everything was working... until the night.

Now, I can't turn it on at all.
If I unplug it and plug it back in, I have the power for ~30 sec and then it shuts off.

What might be the cause? I opened up the case and blew all the dust out of it with air. I sucked all dust from power supply, but nothing of that matter works.

Anybody have any suggestion?
I can probably go and buy some new PSU, but am not sure if it will help or not.

Thank you in advance.