Here are the parts
Replacement parts for FRIGIDAIRE FES300ASD Frigidaire/electric Range | AppliancePartsPros.com

Here is the wiring diagram
http://manuals.frigidaire.com/prodinfo_pdf/Lassomption/318045051.pdf

[COLOR="Blue"]One of the burners on my stove shorted out and made a loud pop. It didn't trip the breaker and the stove still gets power, BUT none of the other bruners will turn on and the oven won't turn on.[/COLOR]
How do you know that it is getting power?
Note: That the timer and oven light only require half the line (120 volts) while the elements need the full 240 volts.
There is not a fuse or circuit breaker in this unit.
If all elements do not work then power is at the top of the list.
Often you can loose half the line without actually tripping the breaker.
Flip the breaker off/on slowly a couple times.
If this does nothing, measure from L1 to L2 to ensure you have the required 240 volts.
[COLOR="Red"]Be very careful 240 volts is lethal!!![/COLOR]

[COLOR="Blue"]Is this a safety feature that when one bunrer is out, they all go out?[/COLOR]
No

[COLOR="Blue"]What else could cause this on this model stove?[/COLOR]
A burned off wire.

This thing is wired where you may be able to use it to troubleshoot.
If both the timer and oven light used to work and now:
Timer does not work - you have lost the L2 side of the line
Oven Light does not work - you have lost the L1 side of the line.

It makes sense if you have a burned off wire.

The burner lights use 120 volts (L1 to Neutral).
The oven indicator light uses 240 volts (L1 to L2)

In spite of the timer and oven light working I suspect that you have a power problem.

Perhaps the wiring diagram is incorrect and both are run off the L1 to Neutral side of the line.

It looks to me that you are not getting L2 voltage you will need a meter to check this out.