E36 doesn't start (alarm problem?)

Hello,
I bought a used E36 (it's actually a 316i Compact from July 1994, I'm in Europe, and I believe that model was not sold in the USA) some days
ago. I was very happy with it, except that, at times, it would not start. I would turn the starter key in the starting position, and nothing (no noise) would happen.
The seller told me that there was an occasional problem with the alarm. It turned out that, when confronted to this condition, I could usually start the car by first locking everything with the remote (red button), and then unlocking everything. It was not systematic enough, though, for me to tell exactly in what situation it arised, and what routine would solve it.
I brought it to a garage, and there it got worse: it couldn't start at all, even with the lock-unlock routine.
There is a key-protected alarm switch near the engine, and the mechanic tried to use this, but the switch appears to be destroyed.
I was told by the mechanic that the alarm system had to be removed completely, and that I would then have a working car, except with no alarm, and that it was the best.
On my side, I was not entirely convinced the alarm system was at fault. The only symptom we have is the starter not working. So why wouldn't it be a starter problem? But the mechanic ruled that out, saying that starter problems are not like that, and that it is the locking/alarm mechanism which locks the starter.
So they are going to dismantle the alarm tomorrow morning.
I am aware this description is probably not very telling, but I was wondering if someone could still try to shed some light on this.
Thanks,
Martin
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I had a similar issue with a 95 325i here in Canada. Your problem maybe the EWS system. It is the driveaway protection computer that cuts off the starter and gas to the engine. I'm not sure if you have the EWS II or EWS I. Mine is EWS II. EWS II has a microchip on the keys that talk to computer. THe symptoms of yours is similar to mine and it turned out to be a broken EWS module. That cost me C$400. + labor + key programming.
Pray it's just the alarm. Good luck.
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