I have bought a used MacBook Pro 2009 from eBay.
I have charged the battery to 100% (worked fine), and booted it. Everything worked, except that I can't boot when on battery. The battery itself is fine, so I can connect the charger, press the start button, and it starts. I can then disconnect the charger, and it will keep running. But without the charger, it will just not recognize the power button press.
I tried resetting the SMC (Shift+Ctrl+Option+Power Button), and resetting the PRAM (Cmd+Option+P+R like 5 times), but nothing changed.
Update: Now it won't turn on even with the battery inserted, and it also does only charge if I try several times to connect the magsafe adapter