Watch out for special digits you need to dial to get outside of the hotel. Your hotel may have an unusual dial tone, or no dial tone at all. Your computer modem may not recognize the odd tone. The modem will tell you it has failed to detect a dial tone. See if you can turn on an Ignore Dial Tone setting.
Many hotels have digital telephone systems.
Do not plug your modem into a digital system. It might fry your modem. Look for a separate analog-line phone jack in the room. It could be installed in the base of the room telephone set or in the wall. If you can't find it, ask the Front Desk where it is.