MBP 13" early 2011, will not start without battery disconect and reconnect

I just received a free MBP 13" early 2011 (MacBook Pro8,1). The keyboard does not respond. The Apple Store said that it just needs a new keyboard. I could install a new keyboard, but the MBP seems to have other problems. It will not start from a powerdown unless I disconnect the power and the battery for about a minute or so. Then the MBP will start either from the internal keyboard or from an external keyboard. Once it is up and running, the internal keyboard does not respond at all-- no keys work --but the external keyboard works fine. Also, a bluetooth mouse does work when set-up to work. Once I have it running, this MBP will "restart", but it will not start from a full powerdown. The battery seems to be charging in that the red light stays on for awhile and then turnes green. The battery only has 177 cycles. I do not think the former owner let the battery run down for a long time. Do I need a new "pram" capcitor. If so, how do I go about replaceing this capcitor. I am fairly handy. I can desoulder and soulder and I know how to use a heat sink. I have a hunch I am not the only MBP owner with this problem.

Thanks