I would probably try disconnecting the router temporarily and connect your computer directly to your modem. This will tell you if the problem is with the router, or if it's somewhere else. It's true that you could have multiple problems, but this will help you to figure out where the problem may be located. You can always connect everything back up again afterwards.
As another thought... some modems have a router built into them. If yours does, that could be an issue as well.
