Computer and Internet use on a boat?

Two weeks is hardly an extended period of time :-)

Get yourself one of those 12 V DC - 220 V AC adapters. They are not part of the usual equipment that charters come with (or privately owned sailboats), but they're worth having. Very useful for charging all kind of electronic devices for which you haven't got special adapters. That takes care of the "power for the notebook" part. Also, always be careful, even if you travel under engines, when charging anything while the engines are off. You need the boat battery in good shape to start the diesel again in the morning.

As far as Internet access goes, I cannot think of anything but a 3G WiMAX card. Although not the quickest connection available, it does the job, and does it solid. Better marinas usually have wireless broadband access (although you will usually need to talk to someone on the reception about that in detail).

As far as notebooks go, several of mine have worked through all kinds of weather, no problems there.

Also, always have the window above the navigation desk closed!! (very important)

I think there are satellite receivers that are made for cars that can automatically swivel to track satellites. There is probably a marine version, but it's sure to be pricey.