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Replacement parts for res7745rq models | AppliancePartsPros.com
I would agree with you that the most likely cause is the timer since you can get it to run just by putting some force on the timer.
The most usual cause of this type of problem is the motor overheating and tripping it's internal thermal protect thermostat but since this requires the unit to sit for a couple minutes so that the thermostat can reset and you can get yours to restart right away, it does not sound like your problem.
Also a good idea to check/clean your vent systen whenever you have to work on a dryer.