The problem for me had gotten so bad, my iLiad wouldn't respond to the power switch at all.
It turns out my problem wasn't in the switch itself, but the plastic slider that you push with your thumb. It wasn't allowing the switch to slide over far enough to activate. I took my iLiad apart, shaved a bit of plastic off of the slider, and it now works like new. Opening your iLiad isn't for the faint of heart, but my iLiad went from almost unusable to working the first time every time.
Now that I have my iLiad together, I realize I should have taken pictures, but I'm attaching a diagram to demonstrate. Excuse my mad gimp skillz.