Turn this to your advantage. Make it a team effort. Talk up the Internet among your hospital colleagues. Find out who's interested enough to support Internet access and form a multidisciplinary team. Make sure at least one information resources person is on the team and listen to what that person says.
Many voices speaking in unison are more effective than one voice.
Include physicians on your team. Administrators pay attention to the needs of physicians. Look for support from your physician customers and keep track of how often they ask you about information that's available over the Internet. If possible, recruit at least two to be members of your team. Ideally, one would be an established physician with solid standing at your hospital and the other would be a more recent graduate of a medical program.