Reset the PMU on macbook when the left shift key is dead
If you feel confident enough the only other way I know is to take the MacBook apart, remove the battery, hold down the power button for 5+ seconds and then put it all back together again. Sounds simple but it could get messy if you haven't taken one apart before.

If you do take it apart you could use this time to try and fix the the keyboard and give the poor thing a clean inside...