The problem with the LF burner most likely is a bad potentiometer. Thermador has redesigned this part and sell it know as a kit included the simmer controller.
In order to find out what is wrong with the oven you have to measure the current drawn by the oven igniter wile it's "on".
- The part number for the simmer control kit is AP3672574
Here are the breakdown diagrams and Replacement parts for THERMADOR PRSG304 | AppliancePartsPros.com