My GE Drier DPSQ495ETOWW will not turn on. If I push the start button I hear verl faint sounding ticking

Since your dryer has a drum lamp, the door switch would have 3 wires on it. One of those wires goes directly to the lamp socket. Ignore that wire. The other two wires can simply be removed from the switch, taped together (and isolated) and retry the dryer (obviously, one should unplug the dryer before doing this or any test). If the dryer runs, you have found the problem. If not, return the wires to their original locations and search elsewhere. It could be a timer problem, a start switch problem, or maybe the "start" switch knob is broken on the backside allowing the knob to slip when you turn it. Good luck and please post further questions.