It is indeed possible that a battery that has begun to expand (some do with age) will cause issues with keyboard and / or trackpad. Is yours an aluminum or plastic MacBook? It is quite easy to remove the plastic MacBook's battery without tools.
PRAM, VRAM and SMC resets are valid techniques for working with your issue.
Best of luck.
There is indeed a story but I ain't tellin'!
It is possible to use the MacBook without the battery though of course you need the power adapter to be plugged in to do so. Not exactly portable. Apple sells new batteries for about $129 in the USA, and there are 3rd party batteries available for about $20-30 on eBay.
I don't need the MacBook to be portable.
I have it plugged in all the time - except rare occassions when I take it to McDonalds.
Something I do not understand from the tech's note:
1. He is waiting to receive the tool he needs to remove the battery.
I live in a rural area; it is the closest reseller for 50 miles and they sell quite a few Macs.
I would have thought they would have the necessary tools.
2. If a tool is needed for removing the battery, I gather that removing and replacing it is not something I can do.
I too am puzzled by the tech's insistance that he needs a tool to remove the battery. It should come out fairly easily with no tool needed whatsoever. It is barely possible that the battery has expanded enough to make it so he has to disassemble the MacBook in order to get it out, in which case you may well have worse problems, such as a bent frame.
Here's the instructions for changing the battery in the 2010 model MacBook. http://www.ifixit.com/Guide/Installing-MacBook-Unibody-Model-A1342-Battery/1667/ 1
Here's the A1342 battery on ebay. http://www.ebay.com/sch/i.html?_nkw=+macbook++battery+a1342&_sacat=0&_odkw=white +unibody+macbook++battery+a1342&_sop=12