Trouble starting 1990 BMW 325ic

[oh6cayuse]

Last fall as temperatures began to fall my 1990 BMW 325 iC (240,000 mi) began to become difficult to start. It used to fire on first turn over, but as it got cooler it needed to crank over longer until when the temperature fell below 50 degrees F, it simply would not start at all even with continuous cranking. As this spring arrived and temps rose significantly into the 50's 60's 70's and now 80's the problem continues with it, now not wanting to start even when in the 60's, it tries, fires occasionally but won't start. I did have to keep the starter engaged the last couple of times that it did start, then it ran rough for a couple of minutes until the engine warmed. I also noticed when I drove it that if I accelerated into a turn that the engine momentarily cut out, then resumed, I have also had the engine sputter when braking while backing up or driving in reverse. I had a spare fuel pump with which I replaced the old one, but found no improvement. Any suggestions or direction to proceed would be most welcome.