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5 Series Beamer
Diary of a Second Hand 15 year old Beamer (Maintenance - Battery Drain included...,
BMW E39 520i year 2000 Engine 1995cc)
M Series.
 
Workshop/Diary - ECU
Poor Acceleration or Pulsed Revs...
I am not sure if it is a coincidence but I left my BM overnight and came to use it the following day and found it could only generate revs between 2.5 to 3K, in other words would be lucky to travel 30 mph with foot fully down on the accelerator, my heart sank and I came close to tears.

Symptoms: On engine tick-over the engine revs and sound in pulses...
Hours of searching the forums and YouTube I came across a 25 minute video that could have been explained in 5 minutes, however not complaining as it saved me a great expense. The video suggested the problem could be to do with the EDU and a corruption in its data and therefore I would be required to reset it to one can only assume to be factory settings. I also took apart my newly fitted 'Wet' K&N Air filter, (a possible cause to the problem - engine compartment Page 54)) and cleaned the MAF and Sensor switch using an air blower (mouth) and checked the vacuum hoses, one looked a little dodgy, a small thin hose on the o/s (right) of engine compartment, it seemed to have a reasonable seal so I have decided to leave it for the time being. 
I then followed the instruction condensed from the YouTube Video:  

The following instruction has been condensed from the video and is a possible solution for this problem:

ECU Resetting to Factory Default

1. Insert key into ignition to 2nd position (with illuminated icons)
2. Push down on Accelerator pedal for approximately 5 seconds
3. Switch off ignition for a full two minutes (leave keys in ignition and stay in vehicle)
4. On two minutes, take out keys from ignition and replace them back into the ignition
5. Start the vehicle
6. Pressing the accelerator, the Revs. Should now be pushing your needle all the way around the clock face.
7. You will need to go for a five or 10 minute drive

The engine Revs. Should now be ‘normal’ and one should get a full range of revs. The five to 10 minutes’ drive is to establish your running data. Personally I found the car to be perky and I was ecstatic with relief to know I was not going to have to pay hundreds of pounds to sort out the problem, (I recollect having this same problem with a previous 5 series and was conned into paying out loads, the garage saw me coming - I like to have think I've learnt from this, however one can forget and does more frequently now as one gets older). Hope this solution helped, it worked for me, well this time at least.
fig.  Limited Revs between 2.5 and 3.5k
Re-programming The ECU (Engine Control Unit)
35
Contents Page
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fig. Source - Example of ECU Unit
fig. The ECU should only be dismantled from the vehicle  and replaced as a last resort.
Another option: Try allowing your battery to go totally flat, I found this allowed the ECU to reset to default over a period of time and on reconnection of a fully charged battery, the BM started and problem was solved.
Workshop