Charge battery a last time outside?

@bjoerns55432 there really isn't a good way to charge it. Your battery is a smart battery, so it does communicate its state of charge to the computers charging circuitry and in a back-and-forth decision is made to charge or stop charging etc.

Granted, I (but this is me and I do not advise anyone to do this or try this) would probably go ahead and connect my bench power supply and connect positive and negative correctly and apply a trickle charge to see if that will charge the battery. It will depend on and the battery controller to accept this as charge or it may not even know I am applying a charge. Of course, I would do this under controlled circumstances and not leave it unattended, monitor heat etc. while doing so. Again. This is me.

For you, I suggest you find somebody that has the same setup as you and ask them to charge my battery in their computer. Otherwise, you'll have to fix your logic board first.