Here are your parts
Parts for Frigidaire AEQ6000ES1 Dryer - AppliancePartsPros.com

Below is a manual. You will have to join the site and be logged in to be able to download it.
http://appliancejunk.com...&id=259;t=1398342688

Looks like the wiring diagram on page 48 is the same as your unit.

[COLOR="Blue"]We've replaced a thermostat, checked everything else we're supposed to, checked incoming electric, and still wont run. [/COLOR]
Which thermostat?
I only see the high limit thermostat and that should not effect the motor starting.
Was it checked with a meter and found to be open?
[COLOR="Blue"]
Before new motor heating element worked.[/COLOR]
This points to a problem because there should not be any heat with the motor off re: the centrifugal switch for the heater should be open.

[COLOR="Blue"]Now we have to manually engage the centrifugal switch to get it to come on[/COLOR]
This is how it should work.
Be careful as having heat with no air flow can cause overheating and blow the thermal limiter and perhaps the hi-limit.

I am assuming that if the unit has a drum light that it works.

To check a few things.
Unplug the unit.
Measure from Neutral (probably best to use the prong on the line cord) to J4-1 on the control board. Should be an an ohm or two (motor windings).
If OK
Measure from L1 to J4-2 on the control board , should be 0 ohms with the door switch closed.
Use the most sensitive resistance scale on the meter. It is also a good idea to short the meter leads together before starting so you can see if there is a zero offset in the meter.

If both the above checks are OK and since you have replaced the motor I would say that the control board is toast re: the motor relay contacts are not closing.

The manual is only available as a .pdf.

Download and install the latest version of Adobe Reader and it should open the file.

I am not sure if you have Adobe as the default program to open .pdf files.
If not I would do that.

I double checked my link to the manual and it did not work so I am try the following if you still do not have it.

http://appliancejunk.com...wnloads;sa=view;down=259

e9e is a line voltage problem.
Check the voltage.
Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
[COLOR="Red"]Be careful as 240 volts is lethal !!![/COLOR]

That is way too high.
I would call your electrical supplier.

Yes it could have caused problems.