If it's fried-shouldn't it throw a code????
 

I jumped the TE1 to the E1 and I get a constant flashing CEL.

My car won't start but isn't telling me where to look. What else can I do to check the codes?

You said you smelled burning when you hooked the battery back up, you might start by checking your fuses and breaking out the test light and checking continuity to relays and sensors.