I'm trying to set up a circa-2003 dial-up modem to receive calls from my laptop so that I can remotely fix problems on one my servers especially if said problem stops the internet connection, firewall ...

Test the modem installation by 1st querying the modem from the 'Diagnositcs' tab in the properties for the modem (Device Manager), and if that works, try dialing out to a cell phone or something, ...