iPad 4 crashes constantly. Bad battery?

I have had issues with my iPad 4 for a few months now and now it is to the point it crashes almost constantly in several different apps, app store, settings etc.

I have tried every combination of restoring, wiping clean, turn off all new features like location services, blue tooth, gestures etc.

My battery seems to work ok but one thing I wondered, is it possible for a bad batter to cause crashes on a iPad, could replacing the battery help?

By the way it acts it seems like it might be memory related, for awhile if I closed all apps out and reset it it would seem to stay up for a few hours before crashing. Now it crashes no matter what. I thought about replacing the RAM but it would appear that you cannot buy the memory sticks.

At this point I think it must be a hardware issue. I will try to roll it back if a jail break comes out and although the bulk of the problems started with the IOS 8 update it has gotten much worse the last month.

Any ideas? I guess I could take it to a Apple store but from what I have been told they don't really do that great a job telling you exactly what the issue is, I don't want to waste my money.