macbook pro doesn't boot unless battery is disconnected and keyboard issues

My early 2011 macbook pro failed to boot recently. As far as I know nothing happened but it's possible my 1 year old was banging on the keys and possibly drooling on it (the older one, a possible witness, is mum on the details). I took it the apple store and they realized it would boot if the battery was disconnected. They offered a new battery but at $130 I wasn't sure I wanted to sink that much into an old computer. I disconnected the battery and booted, however then I discovered several issues with the keyboard. Many of the keys are off or result in multiple characters. As an example, pressing m results in "m;" and b results in "b-" and some like ?< are result in different characters. So, I don't believe it's my battery as it shows full charge and it lasted quite a while recently before this failure. It seems that it's the keyboard but does keyboard problems prevent a mac from booting, or could there be other issues? I'm looking for some ideas before I consider taking it in again.