Networking & wireless forum: Problems connecting modem and router

My ISP is AT&T and I have a Westell 6100 modem. I had a DIR-655 router for a number of years but when a nearby thunderstorm occurred almost a week ago, the router evidently was hit by an electrical shock and died on me.

I then went out and bought a Netgear WNDR3800 router. But connecting the new router and the modem has been very difficult. There is an Ethernet light on the modem and an Internet light on the router, and when the WAN port on the router is connected to the Ethernet port on the router, both those lights are supposed to be on. However with the Ethernet cable sent to me by Netgear with the router, as well as other Ethernet cables I already had and have been using for years ( I had two desktops and a network printer connected to my old router ), I have had trouble connecting he router and the modem.

1) The short yellow cable which Netgear sent me to connect between the WNDR3800 router and the DSL modem does NOT work.

2) Another short yellow cable that I had previously used to connect between my old router and the DSL modem does NOT work when used to connect between the WNDR3800 and my modem.

3) A long blue cable that I have previously used to connect between one of my desktops and my older router, when used as a connection between my WNDR3800 router and my modem, does NOT work.

4) A second long blue cable, which I would swear is exactly the same type as the first one, and which I have previously used to connect between my other main desktop and my old router, when used to connect between my WNDR3800 and my modem DOES work. Unfortunately I need this cable to connect my main desktop to the router ( or directly to the modem when I cannot get the router to work ).

So I need to get a reliable cable to connect my router to my modem that works.

Now my problem is:

1) What is going on with these cables ? Amazingly the cable sent to me by Netgear does not work. Anyone have any idea what is going on ?

2) How do I get a short yellow cable that connects between my WNDR3800 and my modem which is guaranteed to work ? I need the only cable which does work to connect between my main desktop computer and the WNDR3800.

I am a computer geek but I admit I am dazed and confused by this cable problem and why just 1 of the 4 Ethernet cables work as a connection between the WNDR3800 and the DSL modem. I am also confused by why the cable sent to me with the WNDR3800 router fails. Is any of this a problem of the DSL modem and a faulty Ethernet connection ? But if I connect a cable from my computer directly to the DSL modem I have no problems so it seems it can hardly be a DSL modem problem.

Most importantly is there any way to troubleshoot this problem, to determine which component, the new router or the modem, has some sort of defective Ethernet connection to it. I just can not believe that the Ethernet cable sent to me by Netgear would be completely defective ( it looks brand new ), as well as all the other Ethernet cables ( but one ) I have and which I used successfully in the past. I feel that something must be wrong on one of these devices and that buying more Ethernet cables is a waste of money.

I would appreciate the advice of anybody who can help me track down this problem.