Q: 2009 MacBook Pro startup/wake problems

My MacBook works well except I can't restart it without resetting the SMC.

If I put it to sleep it shuts off instantly during the wake up process.

If I shut it down it shuts off early in the start-up process.

It will continue to shut off during start up until I reset the SMC.

To me this seems like a dead battery on the motherboard - whatever keeps the SMC or something else from losing data. But it is weird because it happens even when the computer is plugged in during the shut-down/start-up sequence.

Any ideas? I don't even know if Apple still repairs these.

Thanks!