You may have to consider a visit to an Apple Store to see if a Genius or other product specialist can help you determine if the Battery has swollen to a point where it may be pressing on the inside of the computer, because this can cause touchpad and keyboard issues. Or what is going on. A diagnosis is usually free, and if it is a battery they probably have one in stock you could purchase. If swollen, the computer could be restarted with battery removed, & run on the power adapter to see if the issue was battery, but the power levels and display may be lower, dimmer, slower w/o battery installed.
The Apple Store genius bar is best visited after setting an appointment, you can do that by phone or online. For areas where there is no Apple Store or no genius bar, you can ask an independent authorized Apple service company who probably also sells Apple products at retail. They could determine if the keyboard, battery, or other parts are behind the symptoms you've noted.
Also, if the battery is readily removable by the user (not built-in as newer ones) you could remove the battery and place it on a flat surface, to see if any sides are bulging or warped; if so, discontinue using the battery because it could leak and it can also further damage the computer if it is swollen. Be sure to take the battery along with the computer, not just one or the other.
If the battery is not swollen, put it back into the computer. You could try and see if an SMC reset may help the erratic behavior change to a more normal one. However, the keyboard may also be suspect if these things aren't resolved. A diagnostic test may be required, to visit Apple Store genius is recommended.
•Intel-based Macs: Resetting the System Management Controller (SMC)
http://support.apple.com/kb/HT3964
Hopefully the issue is not too difficult to resolve.
Good luck & happy computing! 🙂
