Here are the parts
Replacement parts for CPLEF398ACA models | AppliancePartsPros.com

Here is the wiring diagram
http://manuals.frigidaire.com/p...pringfield/316255129.pdf

Here is a service manual that may help
http://frigidaireservicetips.co...ngElectricRanges_Rev.pdf

I also swapped the black box (I think it's called an infinite switch) between the left and right side and that didn't work either.
The only infinite switch I can see is for the warming drawer and should not effect the elements.

Any idea what part needs to be replaced?
Sounds like the surface control board is messing up.
I would try cleaning the connectors.
If this does not work then it may be best to call in a pro as this is a fairly complex unit. Unless you have a meter and some electrical/electronic experience.

Connector Cleaning / Checking
Unplug the unit
Open it up
Remove the ribbon cable from the keypad to the control board at the control board.
Clean the edge connector.
If it is the type where there is not a connector just the insulation is removed, it can be cleaned with a pencil eraser. Do not use an ink eraser as it is too abrasive.
Check the tracks in the ribbon cable for hairline cracks. A magnifying glass helps here.
Would not hurt to clean the connector on the board. Use electronics contact cleaner or isopropyl alcohol and a tooth brush. Be gentle and do not reconnect till all the solvent evaporates.
Reconnect everything and give it a try.