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
