Low fuel indicator light

It's not a fuse problem , fuel sending unit in side the fuel tank is bad or the gauge itself is . Your best bet , have it diagnosed by a qualified repair shop .
The fuel level sending unit in the gas tank is a input to the PCM - engine computer . The PCM shares this fuel level info to the instrument cluster over the class 2 serial data network . If a fuse was bad the whole instrument cluster would be out .

Fuel Gage
The instrument panel cluster (IPC) displays the fuel level as determined by the powertrain control module (PCM). The IPC receives a class 2 message from the PCM indicating the fuel level volume. The fuel gage defaults to E (empty) if:
• The PCM detects a malfunction in the fuel level sensor circuit.
• The IPC detects a loss of class 2 communications with the PCM.
When the fuel level is less than 14 percent, the low fuel indicator illuminates.

At the dealer we would hook up the factory scan tool to see if the info from the PCM is getting to the instrument cluster . How to test fuel gauge tank sending unit P0463 GM

Failed Fuel Pump Can Cause Engine to Stall : Pontiac ...

repairpal.com > Problems > Pontiac > Grand Prix
Engine Stall Or No Start Condition on Pontiac Grand Prix. The fuel pump may fail ...No codes thrown... The car finally died on 8th avenue and 30th street in Manhattan. ...1996 Pontiac Grand Prix- 3.1L V6138,920Visitor. My car just decided it ...

Fuel level sending unit. I hope it's not, but ya..... it's inside the fuel tank. Also called the float level.

Not an easy task unless you are ready to drop the fuel tank at home.

Some had a small access hole under the back seat so you could get to it easier, but it's not that easy to get the back seat out, and harder to get it back in.

Hope this helps.

you should have the fuel pressure and volume checked with a gage to compare it to specs.the pressure should be 35lbs and the volume should be about 1 pint in 30 seconds.you could have a plugged fuel filter as well.

may have IPC problem?? but FIRST disconnect 1 battery cable (either cable can be disconnected for this) and touch cables together for 10 seconds. reconnect cable and see if they operate. this is a proceedure for doing a master module reset. this will clear all modules and codes. good luck.

you should have the fuel pressure tested with a gage as if its too low it will not start.without the gage you won`t know the what the pressure actually is.also if you have anti-theft on the car it may have been activated not allowing the car to start.

check fuses and relays

sometimes when the battery is too low the gages will go haywire.check you battery terminals for good conductivity and current levels. sounds like a low current problem.computer runs on 12 volts not 11 or 10. low current will give poor performance and bad electrical response.
try that first then look for shorts under the dash ie naked wires or burnt wires.
good luck.

fuel sending unit in gas tank going bad.

sending unit or float in gas tank, check if any broken wires or well plugged in and then check the float for the gas.