Have you downloaded the latest drivers for your network device?
Modems are separate from the PC and cannot "conflict" in the classic sense. All it is is an Ethernet connection (usually) from the modem to the network port. As long as you're not using a crossover cable, it can't conflict per se.
You did not mention your modem type or brand. If it is a USB modem, there could be a problem with the USB controller. AMD-chipset motherboards do have some USB issues. If this is the case, switching to Ethernet may solve your problem.