My PS2 can’t read PS1 discs (backwards compatibility). Is it that PlayStation made the newer PS2s not backwards compatible...

You’ve replaced the screen with the wrong model or the screen is with the wrong manufacturer (use the model and manufacturer on the old screen) or the connectors are bad or the backlight is broken. Check the connectors , try cleaning them up. If problem persists, replace the screen with the right manufacturer and model and make sure the backlight won’t be broken on the next screen.

Could be the sound card. I have the same problem with my hp (exact same model).

Yes. I have this problem too, but there is a chance that the speakers aren’t blown, but you need to install the sound card. Did you blast loud music before this happened?

The HDD/SDD is dead. Try replacing it!

Your battery probably is bad. Try replacing it. If problem persists, you should try to get the pins that connect to the battery (located on computer circuit) cleaned up. If problem persists, you should get it replaced. Let me know if I’m wrong.