Monitor says no input for months now - which part to replace first?

So my cousin built me a PC back around 2013. I have never upgraded any of its parts and they’ve unfortunately seen a lot of wear and tear, notably, I was careless with dust, water, and there was a time cockroaches were living in the PC parts. I since scrubbed the parts out with alcohol, but I really don’t know if it caused damage.

Flash forward to this year, I was playing Nier Automata when suddenly I started to hear clicking from my PC. I ignored it for half a year, but after a certain point my PC began to freeze, and finally, it would boot up but the monitor would say no input.

Here’s a detailed list of what happens:

• CPU fan spins
• Motherboard lights up
• Graphics card lights up, fan spins
• PSU fan does not spin

(I have tried HDMI, VGA, and to both the motherboard and to my graphics card, and none of these configurations work.)

I would like to try to replace the parts one at a time now. My thought is that if it turns out replacing them one by one doesn’t work, eventually I’ll just recreate a PC with new parts.

For now, which part would you recommend I buy first to try to replace?

I am thinking graphics card or PSU.

Any other thoughts or suggestions welcome.