Sometimes networking problems can be very difficult to isolate. Is it a problem with your ISP on the one side of your router or is it a problem with something on your side? If you follow Gary's instructions to ping your router and you get poor results (such as "request timed out") it's on your side. You can double-check by connecting your computer or laptop directly into the back of the modem. If you get online then you know that it's not the modem.
Here's one example to illustrate what I mean. I was having difficulty connecting reliably to the Internet for two months. The problem seemed to be router-related at first so a new router was put in place. No improvement. Next was a discussion with the ISP and a new cable modem was put in place. Everything was fine for Internet connectivity when connected directly into the back of the cable modem but when it went through the router the Internet connections would drop every minute or so and would sometimes drop completely unless the router was power-cycled (unplugged for 30 seconds and plugged in again). Another new router had the same problem and the company's support was less than supportive, leaving me on my own.
The solution turned out to be related to something called firmware. Firmware is a program provided by electronics manufacturers that places instructions in permanent memory in the device. From time to time a company may come out with a firmware update for a device and either ship it with devices sold after the firmware update came out or offer the update as a download to "flash" the device's memory in order to apply the update.
Routers can have the same model number on the box and yet have different firmware versions encoded in memory that will not be evident until the device is accessed in a browser interface. Most routers have a default address of 192.168.1.1 and the user guide will tell you what the default password is. Once you access the router there should be a tab called "status" where you can find the firmware version (again, check your user guide). *Note: If you cannot access the router when you ping its address you will need to connect it a different way in order to check the firmware or other settings. Connect it directly to a computer instead. This is done by using a CAT 5 cable (mine was a wired router only) with one end of the cable connected to the computer's NIC (network interface card) and the other end connected to one of the router's ports but NOT the port labeled "Internet" or "WAN". Once connected that way you should be able to open a browser window on the computer, enter the IP address for the router, and then follow the steps mentioned earlier in this paragraph.
In my case, I had two routers with the same model number: the old one that I thought was "bad" and the new one that I had gotten as a replacement. Both routers were by the same company and had the same model number on the box but a closer examination showed different firmware versions. It turns out that the older firmware version of the "bad" router worked perfectly to give me a solid Internet connection but that the newer firmware version on the new router caused the frequent dropped connections.
You may ask, then, why the "bad" router worked when it didn't seem to before. That leads us back to my statement at the beginning about the difficulty of isolating problems. The cable modem was actually the initial culprit but it wasn't evident at first so that's why a new router was purchased. It was only after the new router wouldn't work with the new modem and the older router was put in place again that the firmware issue was discovered.
You might not be as fortunate to have two different routers to use for comparison so my advice would be that if you are having trouble with your router check the firmware for your model and then search the Internet for discussions of trouble similar to yours. You might find enough information to use when talking with tech support to insist that their product isn't working correctly and that you want your money back. That's what I plan to do.