The last time we were at the HH resort (Thanksgiving 2006), there was not yet broadband in the villas.

However, we were told that it
is coming, but they didn't know exactly when.
Our choices were dialup

or going to one of the wifi spots at the resort. The most comfortable for me was at Big Murggie's Den (near the registration desk). Another option might be one of the wifi spots on the island, like Mellow Mushroom or Atlanta Bread Company.
In some villas, you are able to get a weak signal, I believe from someplace near the marina, but I wouldn't want to depend on it.