PS2 acts as if button is constantly pressed, even with no controller plugged in
I ordered a brand new controller from a third-party developer, plugged it in, and it worked fine. Strangest thing is that now the old controllers work too, but only as long as the new one is in the socket when I turn the machine on. As long as the new one is there on startup, I can switch them out and they work fine. But the problem persists as before if I don't do this.
In conclusion, I have no idea why this problem happened, but I did manage to "fix" it. If anyone else has a similar problem, I recommend buying a brand new controller, I guess.