I'd call the Cable company to fix that line. Let them check the modem and replace the cable connectors too. You're paying for the service, so make them fix it.
Meanwhile, make sure that the problem isn't with your software. Click Start, Settings, Control Panel, Network Connections, right-click the network connection, properties, and check the box, "Show Icon in notification area when connected", OK.
Now click the Network connection icon on the taskbar, click the "Support" tab, and click the "Repair" button. If that fixed the connection, the problem is NOT the modem.
Download Microsoft's IPConfig Utility for Windows 2k, NT, XP "Wntipcfg.exe" It's just like the "Winipcfg.exe" in Windows98. It beats the hell out of using DOS commands...
Run it to "Releasel", then "Renew" your lease. If that fixed the connection, the problem is NOT the modem.
If the only fix is to unplug the modem, it's either the modem or the cable.