Only charges when powered off...

Hi Fixit!

I have a macbook pro mid-2010 and only charges when powered off. Switched on, the green light stops and switched off, the green / amber light starts.

That is not a problem... But when the power is connected, the power source only says Battery, not charger.

Tried another charger, same result, reset SMC, PRAM.

What I would like is that it only works on power, no battery.

No spills, shocks. no damage, regular usage etc. Thanks!