Dryer will continue to run, in either auto or timer setting, but it will not turn itself off. The timer clock does not move, and the clothes will dry after 40-50 minutes. Does the timer need to be replaced or the thermostat? Is either part difficult to replace? Is there another reason for the dryer to not shut itself off??
Here are your parts
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=DBXR463EG5WW
Since the timer does not advance in timed dry or auto modes I would say that the timer is toast.
You could check this with a meter by measuring the voltage to the timer motor. If it is getting 120 volts and not advancing it is toast for sure.
If you do this be very careful as there is 240 volts a some of the connections on the timer and this is lethal!!!