BMW Repair: No Start, dashboard lights, thick wire

Question
Recently replaced the ignition cylinder on my 1995 740iL.  Car ran fine for 2-3 weeks.  Left my key in the run position overnight.  Next day wouldn't start (not even a solenoid click).  
Tried two different 'spare' keys - same thing.
Charged battery in trunk - after charge it was sitting at 12.6V.  
Re-initialized the transmitter with my remote key.  When done, doors automatically locked and unlocked as book says they will, indicating that the re-initialization was successful.
When I turn the key to the Run position all the dashboard lights come on as usual, windows can be rolled up and down.  Car can be remotely locked and unlocked.  Trunk can be remotely opened.

Things tried:
Tried jump starting it (from +post under hood) - nothing.
Removed cables from both battery terminals - waited 20-30 min - reconnected - No help.
Checked all fuses under hood.
Checked what I think is the fusible link (near battery in trunk?) - Was O.K.
There was 1 large orange fuse rated at 40A - 32V - located near firewall next to fuse box where the relays sit - that was blown.
Have no idea as to what this fuse protects.  Will pick up a replacement tomorrow.
Checked voltage at thick wire running to center of solenoid - got 12.6V
Nothing at either solenoid terminal.  Tried jumping the solenoid with a wire from battery side of solenoid to starter side - Nothing
Tried jumping the center post (hot) on the solenoid to the solenoid post nearest starter motor. - Nothing
Could see that bendix wasn't stuck at flywheel.
Ran a wire from the +post under hood to solenoid post nearest starter - nothing.
Sounds like bad starter?  Why didn't I get even a click out of the solenoid under any circumstances?
Started to suspect Anti-Theft/Immobilizer.   Something to do with EWS?  DME?
Don't know where to go from here to avoid a several hundred dollar bill for towing to dealer and having them hook it up to their computer?
Any thoughts?  Is there a way I can reset the immobilizer?  Do you think that could be the problem?
Can I get error codes using key...or does it have to be OBD or some special instrument?

Stumped, but thanks in advance for any help.

Ron  

Answer
Great diagnostics so far.  Here's my two cents:

1.  replace the fuse.

2.  pull the stater, and take it to a parts shop to get it checked.

If neither of these work, then I'd look at the anti-theft aspects as you call out.  

Good luck!  Id be interested in hearing what it is.