Cruise Control Stopped working

I have a 2000 Intrepid. I start the car and turn on the cruise control. The light comes on for 10 seconds then turns off. I have to turn the car off and on to get the light to come on again. But it still goes out after exactly 10 seconds. If I push the brake pedal before the light goes out then it stays on until I release the brake. I am never able to set the speed even when the light is on. I assume some check is going on during those 10 seconds and something is failing and that's why the light goes off. Does anyone know what part of the cruise control system is failing and how do I test for this failure.
Thanks for your help.

edfromut How does the cruise control behave while you are actually driving? Any other warning lights on?

There are no error codes in the computer. While driving the cruise control will come on for 10 seconds then turn off. I am never able to set the speed.

Anyone have any ideas on what parts may be bad?

edfromut, guess I would start with the obvious, if speedo is working correctly....check brake light switch, vacuum hoses and check for loose or corroded electrical connections or leaking vacuum reservoir maybe you will get lucky, usually these problems will set a code but not always.

Ditto on the brake light switch or that circuit. Cruise may "think" brakes are depressed when they are not.