Powers on only after waiting

After doing clean-up of spill, my macbook pro 13" late 2011 model is in this state:

It will power on using these steps: 1) left unplugged for a few hours 2) hold down power button for 10 seconds 3) with power button still held down, attach mag cord power 4) wait another 10 seconds (power button still held down) release power button - it starts from there. it will gracefully shutdown then power-on with a single press of the power button as long it is not unplugged after a successful start (mag cord light does not turn on here). If it gets unplugged, it will "usually" power-on using the procedure described above - minus the several hour wait. Every other procedure used to attempt a power-on will fail. Once a failed power-on is encountered, the power-on procedure will need to be started from the beginning, including the few hour wait. The battery is for sure old and dead. It will not charge.

Do you think a new battery will correct the system? I would hate to spend money on a new battery only to find out the much more expensive logic board is the issue making it not worth fixing. *Note - once the macbook pro has started successfully - the fan runs like crazy without every slowing down.