You may have a weak
battery, corroded terminal or undersized wire causing a voltage drop severe enough to where the engine
electronics do not have enough voltage to function properly while the starter
motor is cranking. I would first check all your
electrical terminals on your port engine. Chances are your wire was gauged correctly, especially if you used to be able to start your starboard engine first. There is a lesser chance it is an old battery, since you can start your port engine first and have your port engine remain running when you start your starboard engine.
From what you describe, the problem appears to be on the port engine, causing too much of a voltage drop. You should be able to start both engines with a
single battery. This is fine for a twin engine
boat. Just in case someone misunderstands me, I am not saying starting both engines simultaneously, which of course you never want to do.