For some possible solutions check out:
If the warranty on your MacBook Pro is no longer valid, like mine,
don’t worry. Simply take a small piece of paper, such as a Post-It,
and fold it in half. Stick it over the spot on the ribbon cable. Then
reinstall the removable battery. The battery should exert enough
pressure on the piece of paper to keep the ribbon cable working.
If your MacBook Pro is still under warranty, take it to an Apple
service center. While Apple has not officially acknowledged that this
is a widespread problem, it’s afflicted the machines of many owners,
so surely it’s not unknown to them. Demonstrate the steps described
above to whomever is helping you as letting him or her see the problem
as it happens eliminates the guesswork and may help expedite the time
needed for repairs.
THE FIX? I rolled up a sticky note and placed it on top of the cable.
When the battery is locked in place, it puts pressure on the cable,
and makes the keyboard and trackpad functional.
Solution 3 (Apple)
Apple support forum dedicated solely to this issue:
This is a HARDWARE problem!
After playing around with removing the battery and noticing that this
often returned functionality to the keyboard I surmised that this had
some sort of physical aspect. Sure enough, there is a section of
copper colored tape/wiring exposed in the batter slot that is slightly
bowed where it's smallest. When I depressed this with my finger tip on
this portion to basically flatten it out flush against the housing; I
found that all functionality was restored!