Hi there,
I'll start with the daft question first - Is the battery in the keyfob ok?
It will be an aftermarket device, so you'll have to do a bit of digging.
With the car immobilised, does the starter motor turn?
If yes - then the immobiliser is probably interrupting the coil.
If No - The immobiliser is probably interrupting the starter and maybe the coil as well.
Do the other electrics work with the ignition on (lights? Dash lights? wipers?)
If yes then the alarm is going to be between the ignition switch and the engine bay (under the seat? in the rear door bins?)
If you can find out where the box is you can bypass it and remove it.
Wiring is a nuisance to trace, but there aren't many places to hide things in a 126 so that's the best way to find it.