I have a 2003 gmc w5500, the signal lights and hazard lights do not blink, they just stay solid when I turn them on.

Generally speaking, symptoms of a bad or failing turn signal bulb are usually the culprit...in your case, either it's the front left or rear bulb. Varies for different vehicle makes...common signs include:

1. turn signal light staying on solid
2. or blinking very fast
3. or either sides of the bulbs stop blinking altogether.

To test this, make sure you reconnect everything you disconnected.
Turn the left signal light on; go to the front of the vehicle, is the turn signal bulb illuminated? If it lights up, even though it is not blinking obviously the bulb is okay. If it doesn't, replace it- problem solved. You'll do the same procedure for the rear turn signal Is that lit up? If not replace the bulb and the problem is solved.
Another common failure is when the turn signal blinks really fast, same procedure as mentioned above.
If both bulbs for the left side and right side illuminate but don't blink, the problem is in the steering column turn signal switch.
If the left or right side blinkers don't work properly at all...then check the integrated hazard warning/turn signal flasher relay- that may be defective; again, that's usually the case if both sides of the signal light don't work.
If you are blowing any fuses related to the flasher system, you have an electrical overload in the turn signal circuitry.

most likely not a relay but a failed flasher can as the lights are on but not blinking
a relay would not have the lights on

Change the bulb.

Turn signal fuse in fuse block

Check/replace signal flasher. Hazard and signals are on different flashers.

Sounds like a bad ground to me, although i am no expert.
i would be checkinh all connections and take it from there, a little wd40 might just solve it short term.

Check grounding at start of the wires coming from under the truck you will proble find a corried ground wire whitch cause afeed back to other lights thus completing circuit.

that is usually an indication of a burnt out bulb in the turn signal/hazard lights. the other possibility may be a bad flasher. Check all the running, blinker and hazard lights by turning them on one at a time and walk around the car looking for burnt out lights.

hello......this sounds like a flasher for sure! it is cheap and easy too replace.....FLASHER is located under driver's side dash.......round shape, with 2-3 wires connected at 90 degree angle to flasher, good luck

Im Not Totaly Sure But Most other Makes & Modles Ues 2 Seperate Signal FLASHER Units
Your Owners Manual Should Show this As Turn Signal "FLASHER" Located At or Near Fuse / Relay Box This is ASUMING you have Checked The Fuses and Relays