ABS Light Lit, Engine Light Lit - Cruise Control Not operating

I need full make and model # and I can look it up for you.

Crank & cam sensors would not have anything to do with it . Now if the vehicle didn't run (no spark or fuel injector pulse ) sure. The vehicle does start an run , Right ?
What engine does it have ?
Cruise Control Description and Operation (4.2L)
Cruise Control Description and Operation (5.3L)

Your vehicle has electronic throttle control (drive by wire ) do you know what this is. Complex electronic's invloved . The cruise control switches are located on the multifunction/turn signal lever.
The powertrain control module (PCM) monitors the signal circuits of the cruise control switches in order to determine when to capture and maintain the selected vehicle speed. The PCM uses the throttle actuator control (TAC) module motor in order to control the vehicle speed. For further information on the TAC System, refer to Throttle Actuator Control (TAC) System Description in Engine Controls - 4.2 L.

The PCM will engage and adjust vehicle speed based on the information received from the TAC module via the UART serial data link. For further information on the TAC system, refer to Throttle Actuator Control (TAC) System Description in Engine Controls - 4.8L, 5.3L, and 6.0L.

Your best bet , take your vehicle to a qualified repair shop that has the knowledge an diagnostic scanner to trouble shoot your problem .
Complex electronic's involved .definitely need a factory or professional type scan tool .

Your turn signal's & hazards problem is probably the smart flasher ,(GMSF) is an automotive flasher designed to accept turn, hazard,
GM Turn Signal Problem Fix Directional Relay Replacement

Cruise control fuse # 31 10amp located in the under hood fuse / relay box an HZDFL fuse # 40 15amp located in the center console fuse box . If you pull the plastic side panel off of the right side of the console there is a fuse box inside . If the fuse are good the control module could be bad . Could also be turned off because the ABS has a problem .
DTC P1554 - do you know what a diagnostic trouble code is ?

The powertrain control module (PCM) has the ability to inhibit cruise control operation if conditions exist that would make cruise operation undesirable. The following conditions may inhibit cruise control operation:
• The engine speed is too high or too low.
• The vehicle speed is too high or too low.
• The traction control has been active for longer than 1 second.
• The vehicle acceleration or deceleration rate is too high

If the ABS light is on ,there are DTC'S stored in the system . Your best bet , take it to a GM dealer or someother qualified repair shop.

Your onboard computer system has detected a malfunction in one or more of the many systems that is monitored by the computer. You must scan your computer network to find out why it has turned the light on.

Please read this article for further explaination:
Why Is My Engine Light On?

for parking brake and abs check for parking brake switch operation, for abs check with scan tool for any trouble code, for your cruise control unit check for any broken vacumm hoses on the engine, for the ac fan, check the fan motor, relay or fuse.

I would check the ABS sensors on both sides. Those are wires that fit on all wheels to give signal to the ECU for proper functioning of the car. They might just put back the old ones for you . and they should have ben replaces

I have the same problem with the Cruise Control not available coming up but I had a smiliar problem with the ABS and Engine light coming on when battery was pretty much dead, it was hard to steer and brake.. may be something different with your car..

U will need to go to a Kragen or Autozone parts store and have the system tested for trouble code(s), there are well over 100 different code's in the system for failures, the test is free.

The brake and ABS light both come on when you are receiving no speed signal. Most likely the speed sensor in the top of the rearend is bad.

No, it is probably not related. Usually the ABS and traction control light is either a wheel sensor problem, located in one of the wheel bearings, or most likely in the wire harness from the wheel bearing sensor. Remove wires and spray clean with a good solvent electric spray, and check the condition of the receptacle. I have had these problems with my 02 AWD so many times it has become almost routine. GM really have a problem with this type of speed sensor in the wheel bearings. In the AWD model, it keeps the car in FWD if the ABS light is on for any reason. JUNK!