Yes, you are right not to run the dryer by keeping the button pushed in.
Are you going to be doing the work? If so, we would start with check the door switch because it's fairly easy to do and often does cause this problem.
I'm going to check at home later to see if I can get you specific info for this model. I'm pretty sure I have what you need to troubleshoot this if you are doing the work yourself.
Please let me know. I'll check back later tonight.
Do check the door switch to be sure is it has continuity when switched on. It does happen that a wire is disconnected when re-assembling the cabinet.
I didn't find the specific info for your model. However, I got home at 10 pm and had to be up at 5:00 AM (with the change to Day Light Savings Time). So, I didn't have more time to find it.
I will be home tonight at 7 pm and have more time to look. I still think I do have this. I will get back to you with another post tonight. I'm sorry for the delay.
Thank you for your patience.
Here's the wiring diagram for your dryer -
Below items 26 and 30 are two fuses that need to be checked -
Please update me and let me know if you would like more information and/or clarification. I was looking for the specific service manual for this model and it appears there is none (that I have). I think this model was built for Maytag by another manufacturer.
Let's look at some basics.
Can you turn the drum by hand when the dryer is fully assembled? If not, you may have something restricting the motor and causing the overload on the motor to turn it off. This could be that the belt is on wrong, the rollers are bad or any number of other things that could jam it up.
Using the wiring diagram you can run continuity checks to follow the circuit. Something is opening the circuit.
Have you check the timer? If the timer contacts fuse (melt), they will short out the circuit. Will the dryer run if you move the timer to a different setting?
Have you already checked the start button itself?
Let me know how these tests work out.