523i 96 e39 petrol - Starting hickup

Hi guys Can anyone offer me some advise on my starting problem with my 96 523i e39 petrol? The car has 63000 miles on the clockI have just had a full
service ie. Plugs filters and oil. I now seem to have a problem with starting the car - when I start the car (whether it be morning , noon or night) the engine turns over for about three or so seconds and seems to only fire on four cylinders. This is only when the starter motor is running. It seems to be rough until it starts. Once it has started it runs as smooth as you would expect. If i excellerate from a stand still it seems to have a small flatspot on pull away, once past this little spot it pulls fantastically. My main concern is the starting. Could this be from a dieing battery (if so how would I check?) I have just given the car a dose of "REDEX injector cleaner" but so far - no differance. PLEASE if anyone could offer me some advise I would b very greatfull. Thank you for your time and effort. Best Regards Brendan
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