It almost sounds like you have 2 problems each with a separate cause.
Here is a parts breakdown for your unit GE DBXR463EB0WW
Take a look at Item 80 Resistor in the BACKSPLASH section
The timer gets it's power in a different way for the different cycles.
Timed Dry gets power direct from one side of the line (120 Volts)
Auto Dry gets power from the heater voltage (220 volts) so the resistor is used to drop the voltage to 120 volts. If it is open your timer will not advance. Fairly common for these to burn out.
Your having to run 2 timed dry cycles is either not enough heat or not enough air.
The most common cause is not enough air, usually a clogged vent system
To check disconnect the vent and run a load. Does it dry in one cycle?
If yes, clean the vent and check that the exterior vent flap works correctly.
With the vent off, you should have a strong air flow and lots of heat on high setting.
If worried about lint in the house take a pair of pantie hose, put one leg inside the other and attach this to the dryer exhaust. Leave enough room so that it can blow out like a windsock.
There are other things that can cause your problems but I think these are the easiest to check, first. | 
