Dim green MagSafe light and won’t boot, but boots with battery removed

I have a mid-2010 13” unibody that has had a dim green light problem for awhile but still charged the battery after a long time plugged in, and then ran normally. A few months ago the battery was getting frustratingly old so I replaced it.

Dim light/slow charge problem remained, but it worked.

A couple of weeks later it failed to boot after battery was left to completely discharge. Pressing the battery check button with MagSafe attached resulted in all lights flashing 5 times.

Replacing with the old/original battery doesn’t work. But pressing the battery check button just flashes the first battery light, not all 5.

Removing the battery completely allows the machine to boot (after pressing power button for 10 seconds). Machine then runs normally, albeit with fans at full blast and a little slower than normal. It also seems stable (eg I ran a full time machine backup).

Finally, I’m not an expert but upon inspection the D.C.-in/MagSafe adapter board looks like it might have some water damage. The logic board looks OK.

My options at this stage seem to be:

1. Try another battery (seems unlikely to be this as neither work)
2. Try another charger (I can’t find a spare one but could buy another)
3. Replace the DC-in board. I feel like this is doable but given it’s a big procedure I don’t want to do it if the symptoms above suggest this isn’t where the problem lies.

Any advice appreciated!