Most laptops draw 20-30 watts, depending on size, screen brightness, tasks running, etc. I plugged my VAIO into a kill-o-watt once and it was drawing only 18w, my Thinkpad with 15" is probably double that. If you use it for an hour that is roughly 30 watt-hours, which is of course what the OP is thinking of when he is doing his math. I agree that using the rated voltage of the charger is innacurate, but it serves as a max limit. There are plenty of ways to recharge that type of load with a small solar panel and maybe even run it. In fact, there is some good info and products for doing just what you want at this site:
http://www.ecomall.com/biz/sunwatt.htm
Have fun!