I believe that the internet cafe host can set you up with a special card so you can use your laptop on the ship (some wireless connection or something, I don't own a laptop so I didn't pay to much attention). Otherwise there are normal tower type computers in the internet cafe, have never had trouble finding an open station when we have wanted to check our e-mail.
The internet cafe is very expensive in my opinion. The rate I saw was $55 for 100 minutes, $35 for 50 minutes, and (I think) $25 for 30 minutes. I did see a man using his laptop in there, so I'm sure you can get at least a dial-up connection. There are different rates for using your own.
By comparison, I saw on shore in Nassau an internet cafe that was $5 for an hour.