Turn system on, glow stick glows, pilot light lights, but burners not lighting. Help

Exact brand and model number?

Sounds like a Honeywell "Smart Valve" ignition system, if a hot surface ignitor is used to light the pilot. These have a history of failure within the combination ignition module/gas control. Try this: press inward on the square 4-pin connector on the Smart Valve while the pilot is lit. If main burner operation is achieved, the control is bad.