MacAirboots w/ battery disconnected, won't boot if battery connected

MacBook Air 13" mid-2011 4,2 A1369.

MacAirboots w/ battery disconnected, but won't boot if battery connected.

Detail: fairly new battery, 288 cycles, replaced by Apple.

Battery charges OK, 76% battery health.

MacBook Air does not power on, completely dead.

Magsafe orange then green -- looks like charging OK.

I opened the case and disconnected the battery. Then, when plugged in to Magsafe (green) with NO battery connected, it powers on and boots normally every time.

If I reconnect the battery, won't boot. If it's plugged into Magsafe and battery is reconnected, I can boot just once. Then after shut down it's dead. To boot again, I have to disconnect the battery.

Have reset SMC and NVRAM. A few days ago there was a little water spilled on upper left of keyboard cleaned up immediately. Computer started behaving oddly (put to sleep on battery, would reboot) *before* this happened.