First thanks for your replies,
Big Evil, yes indeed my battery was defective, and with the recent cold days we had over Dublin (Ireland), I think its weakness has just become more visible.
I replaced it today with a battery of a larger capacity (strangely the 100Ah bosch one was just as expensive as the 70Ah I was recommended to buy).
The ELM 327 I ordered finally arrived ! but unfortunately it seems that my car is not ODB2 compatible
(carsoft says unable to establish connection, please check the cables etc. even though the ELM is working perfectly).
I read over the web that unfortunately, if US versions of the BMWs in 1996 were all compatible with ODBII, it wasn't the case in the european countries.
Manolito, yes my car is a E36 323i of 1996. Don't know if it was sold in the US at that time, it could be the reason why you never heard of it.
Yes I carefully examined the rubber boot, it was cracked and I replaced it about 2 weeks ago. But as the car is not starting at the moment I couldn't notice any change yet (I had the jumping problem on 1st gear before which is likely to be due to the cracked rubber boot).
Concerning the loud noise, it is kinda hard to describe properly but it is like when I push the accelerator the engine sound turns loud like if air was blown into it but with too little petrol. At idle it was running perfectly but as soon as I got too far in the rpms, I had the noise and a stall in the power / rpm increase. It just feels to me like all I could control with the accelerator pedal is the amount of air to inject in the engine, and it is just like if the petrol quantity injected was only the small amount controlled by the idle control. It is just a feeling I'm not sure it is really what's happening.
Now to focus a bit of the engine starting problem, with the new battery installed the engine won't start properly either. It runs at about 1000rpm for 3 seconds with a dodgy sound and then stops (kind of plom plom plom sound).
Someone told me this could be due to a disfunction of either the camshaft sensor or of the crankshaft sensor.
What do you guys think ? Could one of these two sensors be at the origin of all the troubles the E36 is having ?