Sorry to hear, that's aweful. I haven't had any such issues with my GF2, and i'ts bounced around in my camera bag quite a lot. Such a solidly built little camera I expect to handle itself well.
It would be worth checking that the battery does indeed have power in it, unless you've tried with a couple of batteries. If you can find a little light globe, LED or something similar and touch it quickly onto the battery terminals (the two outside terminals are power, ignore the middle two) to be sure there's actually juice. Be careful not to short them together though, lithium's don't like that.
This is worth trying even though the charger says it's done, depending on how the charger is designed, it may show charged with a collapsed battery.
Also if you don't have a spare battery to try, stick some tape over the middle two pins on the battery and try it. This is in case that battery's internal meter has got out of whack and tells the camera not to start, see if the camera starts at all then. Mine starts up and then says the battery can't be used, but at least it starts up. (it's fine again once the tape is removed).
Otherwise, have you tried powering up with lens removed, and with sd card removed? It's worth trying anything like that, in case a peripheral is blocking it.
If nothing helps, I don't suppose you've got some warranty... ?
Andrew
