Why can't my PS3 enter standby mode?

When I power on my PS3 40GB (CECHJ04), it seemingly acts fine, but there is no signal getting to the TV. I’ve tried changing TVs, HDMI cables, component, nothing. Tried to reset the output settings by holding power until the second beep, cleaning the inside, all for naught.

After trying to get it back running for a few days, I also noticed that there’s no red light whatsoever. It just doesn’t glow red (or yellow) and it can’t enter standby. Atleast I am assuming so, as I can’t see anything changing on my TV. Also, it doesn’t turn off by itself, even after hours on end. The fan is just spinning quietly, the LED is solid green and the disc drive functions properly.

So, should I even bother buying a new HDD, applying new thermal paste or changing the motherboards battery? I don’t wan’t to use it myself, just want to fix it because I like to repair “retro“ consoles.