Here are your parts
Parts for Frigidaire FEFL78CBC Range - AppliancePartsPros.com

Here is the wiring diagram
http://manuals.frigidaire.com/p...pringfield/316255355.pdf

Since stove is totally dead the problem is probably power related.

How did you check the circuit breaker?
Just looking at it is not good enough.
Also before doing anything try to find out what the bang was.
Remove power from the unit and check the bake and broil elements for a blow out.
Remove the back and check the wiring .

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]

[COLOR="Blue"]Could the light socket cause the whole stove to be inoperable?[/COLOR]
I doubt it.

Here is why I think it is a power problem.
If you look at the wiring diagram you will see that the stove top elements and the oven control and it's elements are separate entities.

The stove top elements require 240 volts (L1 to L2)
Their surface indicator lights require 120 volts (L1 to Neutral)
Since each one has it own analogue control (infinite switch), it is unlikely that they would all go out unless you have a burned off wire in the unit or there is a problem with power getting into the unit.

On the oven side the elements again require 240 volts.
But the control board runs off of 120 volts, again L1 to Neutral..
The oven light also runs off of 120 (L1 to Neutral).

I am a bit confused as you said " The bulb however, still works." but originally said nothing works.
Did you check this bulb outside the unit?

So if I understand your original post correctly that nothing works then my guess would be that you have lost L1 voltage as it effects all devices in the unit.

Then I would do the procedure outlined in my first post.

Since you have 240 at the termonl strip there must be a problem with a wire that is common to both the stove top elements and the bake elements.