Gas gauge broken in 2005 trailblazer - 2005 Chevrolet Trailblazer Ext

Hello, this problem is due to a failing stepper motor. The stepper motor is the motor behind the gauge that controls the movement of the needle. When a stepper motor begins to go out it will cause the gauge needle to stick, skip around, stay at zero or max out on the gauge. The only way to fix the problem is to replace the stepper motor with a new one. While replacing one motor it is best to go ahead and replace them all as the others will go out in time as well. Your cluster will have one motor for each gauge. Here's a link to a page showing exactly how to replace a GM stepper motor and where to get the correct parts to do the job! DIY Finally How To Repair GM Instrument Cluster At Home Speedometer And...

IF the needle is way off and pointed down or way off to one side then the most common thing is the cluster being bad, If you do not have a bunch of aftermarket stuff and not a huge amount of miles then I think there is a special policy for this at a GM dealership, it will be done for really cheap, you will just need to pay for labor.
If the guage is just not working then the most common thing is the level sensor inside of the fuel tank. This will set a code in the pcm, but will not turn on the check engine light so you will not know the code is there. If you take it to autozone or one of those places then they should scan your car for free and tell you if there are any codes.