First I’m going to ask if the new router is wireless or not?
Also rebooting everything can sometimes help (if you haven’t already).
I’m also going to assume you’re on Windows (Vista, XP)?
I’ll just mention a few things since this type of thing can have many different causes:
1.) Make sure ethernet plugs are fully plugged in. Sometimes even when they’re fully plugged in they sit just slightly crooked to cause problems. I usually unplug all cables and then re-plug them in when I have a problem. It’s a quick and easy way to make sure that is or isn’t the problem right from the start.
2.) It’s possible that a Firewall or Anti-Virus could disrupt this. Especially since the router is new. You might have to allow an exception in this case.
3.) I would update the firmware on the router to the newest from the manufacturer. Most new hardware that you buy has been sitting in a box somewhere for a while typically. So the firmware is probably out of date. You can usually search for the model you have on Google and then find the latest. Some with have an installer that you can just double click. Others will have a file that you will manually have to load onto the router itself. Some routers can be accessed wireless (if they are wireless) such as my airport express. You should also be able to access the router by hooking an ethernet cable into the router and then either typing in the address or ip for the router.
Post back after you try some of these so we can zero in maybe on what’s causing it.