I got this information from the Xbox website.
I take no credit, but I am sharing it here.

Symptoms

Four lights around the power button flash red on your original Xbox 360 console. Four flashing lights mean the console doesnt detect an audio/video (A/V) cable.

Solution 1: Disconnect and reconnect the A/V cable

There might be a problem with your A/V cable. The A/V cable connects the console to your television.

Let's see if disconnecting and reconnecting your A/V cable fixes the problem.

To disconnect and reconnect the A/V cable

Turn off your console and television.

Disconnect the cable from the A/V port on the back of your console.


Unplug the A/V connectors from your television.


Reconnect the A/V cable to the A/V port on your console.


Plug the A/V connectors back into your television. The A/V connectors match the colours of the component video, the composite video and audio ports on your television

Turn on your television and console.

If four lights still flash red, try the next solution.



Solution 2: Try a different A/V cable

Try using a different A/V cable to connect your console to your television.

Using a different A/V cable is the best way to figure out if there is a problem with the cable or with your console.

Here are a couple ways you can obtain a second A/V cable:

Borrow a friend's working A/V cable.

Buy a new Xbox 360 A/V cable from a store or from the Xbox 360 online catalogue.



This information is confirmed by Xbox and should fix your problem.

If not, then you might need it repaired by Microsoft.