Its going to depends on what you mean by "modem". If it is a true modem like a cable modem many times the issue is they have locked it to only work with a signal mac address. The common solution is. Turn everything off, turn the modem on, turn the router on, turn the PC on.
Now if the box the ISP provides is actually a router then you need to be careful that they are not using the same ip blocks on the wan side as you use on the lan side. Directly plug your pc into the ISP box and see what you get for a IP..should tell you very quickly if they are using the same as you.
Exactly, my "modem" has 3 ports for pc's on the back and was the same address as my router when I checked. The provider changed something and my router quit working, must have pushed out some update.