Hi,
Could you let us know some details about your system please? System manufacturer and model number? Motherboard make and model number? Modem make and model number?
I've come across a couple of 'budgetty' motherboards which are prone to problems like this when connecting an ADSL/Cable moden via onboard Ethernet. The systems using them were both fine with the initial Windows XP install, but following a full 'Security Update' of Windows XP neither would retain the internet connection. Motherboard driver updates or BIOS updates did not correct the problem, and rather than forgo the Windows Security updates I decided to disable and uninstall the onbard Ethernet, and install an Ethernet add-in card in its place.
That corrected the problem.
Your own problem, of course, may be something completely different. There's never any "One Final and Complete" answer to PC problems, after all!