Welcome to cruise-chat.
All personal computers have to access the internet through the ship's internet connection which means you'll still have to buy internet time from HAL. It is the only form of internet available unless you are in a port where you can get a 3G connection or find a hotspot.
Cellphones can be used and will accrue international roaming rates, but smartphone features can be used depending on the cell phone carrier. In this case the ship doesn't charge anything and all extra fees are billed through your cellphone provider.
I bring a netbook on ships and use it with the ship's wi-fi connection. They will also have an internet cafe with several desktop stations you can use. It's really a personal choice on whether you want to lug a laptop with you. Bottom line is there is no way to get internet on a ship at sea without paying them to use it.