Here is the parts breakdown includes a wiring diagram
Replacement parts for MAYTAG PYE2000AYW Dryer - Ele | AppliancePartsPros.com

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[COLOR="Blue"]I ordered LA-1053 (Thermal Fuse Kit) and LA-1008 (Rear Roller Kit) and I find that the Thermal Fuse on my dryer has four (4) connection and the one I got from you guys only has two (2).[/COLOR]
I think you are confusing the thermal fuse with the thermostat (cycling).
The cycling thermostat has 4 connections. One set are it's contacts, the other set is an internal heater. It is turned on to add heat to the thermostat and causes the unit to run cooler re: dedicates etc.

[COLOR="Blue"]In checking electrical connections I believe that the thermal fuse is working, but when I start the dryer it runs for about 5 minutes and then shuts off. If I wait till I hear a click (about 2 minutes) it will run for another 5 minutes.[/COLOR]
If a fuse is blown it will not work at all, if this is the fuse on the blower assembly.
If by shutting off you mean the unit stops running (no motor), then your problem is not a thermal fuse as neither of them will do this.

[COLOR="Blue"]The original problem was that it just wouldn't dry the clothes.[/COLOR]
The most common cause of this is a dirty vent system or it's louvers will not open.

[COLOR="Blue"]Is there another fuse link that I do not see. The High Limit fuse fit so I have used that part of the Kit.[/COLOR]
There are 2 fuses. The one on the blower kills power to the unit. The one on the heater kills power to just the heater.
From what you said above I think you must have replaced the heater fuse and it's high limit thermostat.
Correct?

When the unit shuts off can it be restarted right away or do you have to wait several minutes.
If you have to wait then it is probably the motor is overheating and tripping it's internal thermal protect. You then have to wait for it to cool down and reset.

[COLOR="Blue"]While I had the drum out and everything running like normal the heater coils would just turn on for about 5 seconds and then go off wait about three minutes and then the heater coil would turn back on but the unit never shut off.[/COLOR]
This is probably normal. When the drum is out there is no air being pulled over the heating coils so the heater will not cycle normally.

[COLOR="Blue"]I guess I could have not got the drum on the rollers or something that might be causing the motor to over heat so I will try take it back apart and checking that.[/COLOR]
Try turning the drum by hand in the correct direction, it should turn fairly easily. You may want to try this on a couple other dryer, just to get a feel for it.