Two words (and a digit): GoPro Hero 2.
Get the motorsports edition as it comes with a big suction cup that will stick to just about anything, as long as it's not porous. Reportedly even to the outside of the aircraft at typical flying speeds - but I have not worked up the courage to try it for myself so far. It also comes with various stick-on mounts and a variety of mount conversion hardware so it's extremely versatile in how and where to mount it.
It'll only cost you a little over an hours worth of flying. Time you have probably wasted already by messing with that laptop/webcam solution. And a solution that may save money in the long run - what if there's a bit of turbulence, the laptop drops and breaks? The GoPro comes with a polycarbonate housing that's probably strong enough to drive a lorry over.