I'm guessing from the above posts, that the  battery in your fob has failed.  
Renew the battery & hopefully the cental locking will work.
Do a reset  on the door locking by sitting in the car with ignition on II & press the locking button on the fob & all doors should lock & then unlock .
Remove key from ignition  . . . . then using the fob, operate locking again to lock ( you can do this from inside or outside the car)   . . .
Then operate to unlock  . . . then  put key back in ignition & it should start hopefully  
Had this happen on my last 2.6    but can't remember who advised this solution  . . . but it worked 
Sounds crazy . .  . but worth a try   
 
The immobiliser and central locking/alarm are two entirely independent things (on post 1995 Omegas), each with their own ECU.  The fob is 100% purely for CL/Alarm, and plays no part in the immobiliser function. Therefore a flat/missing fob battery will not cause an immobiliser issue, though will set off alarm is you have to unlock/open car with mechanical key.
Hope that clarifies 
Just thought this may be worth a try TB as it sorted my last 2.6 MV6 when this imobiliser problem occured.
I also understand your knowledge of this sort of thing is second to none  . .   but  . . .
It also worked and got  Toledodudes car  started when I instructed him over the phone ( although that one did go on to have a major ECU breakdown in the end )
I understand that the key fob battery has nothing to do with this but ..my point was that the OP cannot do a re set of central locking when the fob will not work.
Cure for mine was : ignition on  . . . press lock on fob  to re set  . .  doors lock & then unlock (re set )  then
 remove key . . 
lock doors again with fob with key in your hand  . .  then open doors with fob in your hand .
then car started 
 
  
 
As said sounds weird  . .  but it has worked on 2 cars to my knowledge.
For the life of me I cannot remember who on Oof suggested this  
 
 
Must be worth a try for the cost of a fob battery 
 
 