Light for cruise not coming on and cruise not working

Check the brake light switch and fuses.

If cruise control main light comes on but you cannot set a speed (no set), you could have a bad brake pedal switch.
(If the cruise control light comes on, chances are that it is NOT a fuse issue).
Some vehicles have two switches (one for brake lights and one for cruise control cancel) and others have a multifunctional, single switch.
The function to cancel cruise control is very sensitive so it only takes a small movement of the pedal to cancel cruise control.
You can try lifting on the brake pedal while trying to set the cruise, but this does not alway work. Replace switches are pretty cheap (less than $30) and pretty easy and quick to replace.

make sure 3rd brake light works, most likely you have a code in the EBCM (antilock brakes), some codes disable the cruise control, possible vehicle or output speed sensor or wheel speed sensor.

The cruise is not separately fused.

Your dealership should have seen any underlying codes. Most Cruise controls I've worked on are used on the vehicles vacuum. that is where i would start, because on a grade your engine uses more vacuum pressure thus taking from some where else.

Has your check engine light been coming on? The cruise will not work if there are certain fault codes stored in the computer. The next questions are: has your airbag light been coming on? Does your horn work when the cruise is not working? These can be clues to a bad clockspring assembly in the steering column - which would affect your cruise.

Make sure the cable from the cruise control motor to throtle is not broken or unattached.

Sounds like a voltage problem. Have Charging, Starting , and battery system load tested.

take it to the work shop

You may have a faulty brake lamp switch at the brake pedal. If the brake lights come on (via a bad switch), the cruise will cut off.