Here are your parts includes a wiring diagram.
Replacement parts for FRIGIDAIRE FDEB34RGS1 Frg(v0) / Free Standing Dryer | AppliancePartsPros.com

Here is a better copy of the wiring diagram but it is for a RGS2 not a 1.
I think it is the same.
http://manuals.frigidaire.com/p...df/Webster/131953900.pdf

I doubt you need a motor.
I would start by checking the thermal limiter, Item 36 in Section 1.
It should be o ohms at room temperature.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it so the thermal limiter blows.

Just in case it is not a grounded element.

Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system, this is often the cause.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut).

Also this unit uses a center drum bearing which can often cause squealing so check that for wear. If OK clean out the old grease and use a high temperature grease to re-lube it. Be careful with the ball bearing (Item 5 in Section 1) once released it likes to take off and play hide and seek.
The above is just a suggestion since you have the unit opened up already.
You probably did this when you replaced the belt but I thought it was still worth mentioning.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.

There is a good STICKY at the start of this forum about it's use.