Four lights around the power button flash red on your Xbox 360 console. Four flashing lights indicates that the console does not detect an audio/video (AV) cable. Make sure that the AV cable is correctly connected to the Xbox 360 console. Disconnect the AV cable from the Xbox 360 console, and then reconnect the AV cable to the Xbox 360 console, from here I know you already tried all that but do wanted to add it for completion sake.
If the 4 red lights continue to flash, try wiping the metal area of the AV pack with a dry cloth. The metal area is the end that plugs into the console. Wipe the metal area thoroughly, and then try the AV Pack again. If the AV cable is correctly connected but the four red lights are still flashing, substitute a different AV cable if you have one available.
Flush the cache memory by following the steps below:
-Shutdown your Xbox 360 console
-Press and hold the SYNC button first, then press the POWER button together.
-When your console reboots, let go of the POWER button BUT keep on pressing the SYNC button
-When your console has completed rebooting, all cache memory will be flushed.
from here. But, that is a pay site and all the information is available in the public domain.
Check on here for further information and how to determine secondary error codes and see what you come up with. It is my gut feeling that you do have an overheating problem (but try the easy stuff first) If your error is caused by overheating, the kit should fix it. Of course make sure that your Xbox is not covered by warranty or anything like that. You would not want to void it. Also make sure that you clean it well of any dust and obstruction and that you provide good air circulation to prevent any overheating issues.