The hodge podge of gear means I can't be sure. Now if your software does accept an IP address you could put this machine into the DMZ entry of your Xfinity router. Be aware I don't explain DMZ or what page of your router manual here. You must be conversant with your gear and network.
As to the WiFi as it is, I take it this does not work so the step to anywhere is a bust until you fix that. I'd use a powerline bridge instead.
My end goal is to be able to access a device (a calibration station at work) from anywhere. I have reconfigured a Linksys WRT54G2 v1 into a WiFi adapter for the device (no USB or WiFi card on the device), and have a Buffalo AirStation WHP-300HP as a repeater, because the signal is too weak to reach the room the device is in. The wireless network this setup is connecting to is the secure side of an Xfinity router. Is it possible to connect through all of this to the device (which requires software on my laptop to control) from any network, anywhere?