2004 Chevy Trailblazer LS - instrument panel gauges

GM instrument clusters 2003 - 2006 had problems with gauge stepper motors . Having the vehicle hooked up to a professional grade or factory scan tool that can view this kind of data would be necessary ! This information comes from the PCM/ECM - engine computer over the class 2 serial data bus or network communications .
How to repair GM Instrument Cluster Speedometer Gauge Stepper

This sounds like the fuel level sensor in the gas tank is going bad, or there is a bad ground at the tank. A technician using a scan tool can monitor the actual fuel level data to verify.
Another possibility is a bad stepper motor in the instrument panel, each gauge had a stepper motor to drive the needle.

I'd use a couple of resistors representing full and empty. Take connector loose from fuel level sending unit at gas tank, two wires, use resistor between the proper two wires, turn key just to on, you shouldn't have to start it. If gage reacts properly to both resistors, I believe the problem is the sending unit in the gas tank. If it still doesn't function properly, have to check wiring circuits and instrument cluster. The resistor ohms, 16 ohm--and 158 ohms. These are just generic specs.
Some ford instrument clusters can do a self test. The only problem I have is, I don't which years this applies.
With the engine off, depress and hold the odometer reset button. Turn the key to the run position and hold until the gages sweep, within 5--8 seconds. Depress the reset button once to advance to each stage of the self test. Turn the ignition to the off position to exit self test. This test is w/o outside input, so if all gages sweep except the fuel gage, I suspect the instrument cluster has a problem. I'm not sure if your instrument cluster has the self test ability?

the instrument cluster has a fuse that will blow there should be one under the dash around the drivers side or on the side of the dash or in the glove compartment there is also another one in the engine bay as well its not uncommen that u may have to remove a cover panel or two if its under the dash.

Pretty common problem with these. Here's a guide to learn how to fix GM instrument clusters yourself, I used it to fix mine and it worked great.How to guide for Trailblazer instrument cluster repair

Usually, the stepper motors that drive the gauges fail. There are instrument cluster services listed on Ebay.

the fuel level gauge just went out na dthats why the light is on. to replace it you have to replace the entire sending unit. cost is $500.00 plus to have replaced. if you can live with it and keep check on your milage, I would wait for the pump to go out.

Could be a
1. Fuse - not likely, I'd expect other instrument panel problems.
2. Broken wire from fuel gauge
3. Bad fuel sender in fuel tank. Normally requires dropping the tank.

Vehicle is not that old, would think it is still under warranty?

check to make sure a fuse hasnt blown or a relay

your relay is going bad, replace it.