About 10 years ago, my Mercruiser guy swapped out the dizzy for a newer style under a warranty/ recall - it was, I assume due to the moisture you mentioned - I had to clean that old dizzy cap/ rotor contacts all the time back then to remove the white fuzzies. After the swap, it has not been a problem at all.
Yes the old design would of been a concern for your starting/running issue you seem to be having now.
Checked the water fuel separator. All was clean.
Was the filter still completely full of fuel when you removed the filter?...And if you haven't yet, be sure you install a new one too of course.
You'll want to clean the throttle body, flame arrester, IAC motor (Idle Air Control) and all passage ways and replace the IAC muffler if your model has one located in the T/B housing.... I'll take a look at the shop manual and do this.
The passage ways to clean would be the dotted line from item number 6 on over to item number 16ish ,
http://www.marineengine.com/parts/mercury_marine_parts/sn/0M634400/444206HRS/8093_85
The IAC muffler is item number 6 that needs to be clean/replaced and ensured is still in place every so often as it does disappear into thin air at times...Clean the throttle plate and inside housing too the best you can.
This guy replaced his which may be helpful in your case too,
https://www.youtube.com/watch?v=ROOlvjx38BU
You don't have to remove the T/B housing to clean as described in the following link but there are many how to videos of how to clean throttle bodies on cars/trucks that will help give you some ideas...,Edit: The links not working here on this website so you'd have to search online ( MerCruiser Throttle Body Factory Service Reference 5.0 5.7 6.2 )
http://downloadrepairmanualpdf.blog spot .com/2014/01/mercruiser-throttle-body-factory.html
Check fuel pressure as it may be a bit to high or low....You ought to have a fuel schrader valve on the fuel rail making it easier for you to check once you get a fuel pressure gauge that fits your schrader valve. Will look for the Schrader valve - I have a full pressure gauge that I can retro fit to work. You know where this valve is ?
The valve ought to be on the fuel rail center that runs between the two sides...The valve is covered by a black cap that resembles a tire valve cap...See item numbers 18 and 19,
http://www.marineengine.com/parts/mercury_marine_parts/sn/0M634400/444206HRS/8093_90
What is the proper reading ?
Right around 43 PSI +/-5ish psi but usually 43 psi is with the vacuum hose removed from the fuel regulator at idle RPM.... item numbers 19 and 13,
http://www.marineengine.com/parts/mercury_marine_parts/sn/0M634400/444206HRS/8093_60
Are your battery Volts and Cold Cranking Amps up to specifications for your engine model ? How do I check this ? I have a good voltmeter - where do I attach ?
Connect your meter right to the battery posts but make sure all the cable connections look clean and tight and check the cable connector ends too if you think it becomes ever needed...An auto store could test the batteries too but having the following tool comes in handy pretty often as well,
https://www.harborfreight.com/digital-automotive-battery-analyzer-66892.html
One of your MPI sensors could also be just slightly out of normal sensing value ranges affecting the clod start feature...I agree Such as the Engine Coolant Temp sensor I just had work done on my cooling system - my mechanic troubleshot and replaced my heat exchanger, where is the engine coolant sensor ?
The coolant sensor will look like item number 6 and it will have both a Yellow and Black wire coming out of it.
http://www.marineengine.com/parts/mercury_marine_parts/sn/0M634400/444206HRS/8093_190
^ Being you have closed cooling the coolant sensor might be elsewhere of the thermostat housing such as the front of the intake manifold so be mindful of that small possibility.
The T/MAP sensor, 'Which two ways to inspect those would be to use a marine scan tool while cold both engine off first then right at engine start up....And if you don't have a scan tool then multimeter could help some too.
Just for quick reference the T/MAP sensor is item number 8,
http://www.marineengine.com/parts/mercury_marine_parts/sn/0M634400/444206HRS/8093_90
When was the last tune-up done? Not in a loooooong while. Have new plugs, but could use ignition wires, cap and rotor ( actually bought all the parts just have not had time to replace. The correct gapped spark plugs where installed ? Yes ..... What does the spark plugs look like right now? I'll check Are they rich looking at all ?.
Got to get your priorities in line here...
Time to get to work on the boat and not at your actual work that helps pay for the boat....Lol...Just kidding.
A preventive maintenance type tune up may be your answer but even if it isn't doing it would help give you the indication if further diagnostics are still needed.
The very first time she did not start right up, it was right after a really COLD snap here - I initially though of a sensor.
Yesterday, after not using her for a week - she initially started right up. I turned her right off, and then when trying to restart - it was difficult. Had to do the neutral/ throttle thing.
This am - the boat started right up, although she does surge up and down at idle when cold ( she has always done this, but I think a little bit more lately ).
Then, she ran great for a few hours.
The first time she did not start up, it was right after a really COLD snap here.
Being the engine was started and turned off quickly and coming right out of a very cold spell this time of year....'There's a chance you may have caught an slow moving IAC motor right between a point that it was unable to provide the correct amount of air to help start the engine on it's own and by you opening the throttle up a bit helped get the engine started in turn giving the ECM a chance to reset the IAC motor to it's correct placement.
It typically recommended (especially on cold engines/days) that you cycle the key on and off slowly 2 times before cranking the engine over to start in-turn giving the fuel and electrical component systems to prime themselves up....Even your car/truck would like you better if you first key up until the fuel pump turns itself off within the first few seconds before cranking over to start.
