Chosen Solution

iPad 2. Began with shorter battery life, then shut off. Recharged very quickly. Then later only boot when plugged in, and finally nothing. How should I proceed. Apple store of no help. Thanks BT

It sounds like you have a dead battery. This requires removing the screen, hopefully without damaging it and then removing the logic board etc. It’s a fairly involved repair. I suggest you check out this repair guide to see if you are comfortable doing this yourself or if you prefer to have it done by a shop. All the tools and parts are listed in the guide.