frustrating communications (port?) problem

i bought a new computer running XP. I have a wireless connection to a modem located in another room. The modem is connected to an ADSL line. The signal to the modem is strong; in fact i can connect to the internet from my old computer which is right next to the new one. I have tried many times with my ISP help center to ensure my network connections are proper. Still I can't connect.

My network neighborhood shows three networks. The wireless network that connects my computer to my modem, the network that connects to the ISP, and a local area network. I suspect (since I can find no other problem) that there may be an issue sharing a communications port between the LAN and the ISP connection. Is this possible? I tried to delete the LAN but the computer says that it can't be deleted?

I previously estalished a COM connection between the old and new computers to run the File Transfer Wizard.