To troubleshoot, you should:
1. Consult your owner's manual: It will show you the fuse box diagrams and locations, including descriptions of what each fuse protects. Look for fuses related to the Body Control Module (BCM), as the cruise control often ties into that.
2. Check all fuses related to the BCM and power distribution: Don't just look for blown fuses (a broken filament), but also visually inspect for any corrosion or damage to the fuse or its holder.
3. Check the cruise control relay: Your owner's manual or a repair manual will show you the location and how to test this.
If all fuses and relays are fine, the problem likely lies within the cruise control system's wiring, switch, or the actuator itself. You'll likely need a professional mechanic or a detailed wiring diagram to diagnose further.