94 1.6L Mx-3 Random Shut off in wet weather

[p_p_pi]

Car is completely stock. (about 160K miles now)

On heavy rainy days, it would randomly shut off while driving (initial start-up is fine though). When i try to start it again, the engine cranks fine but won't start. Then after a few tries, it would start again. Then it would shut off again; and i have to wait/try for another 5 or 10 minutes to start it again. It happened 3 times today!! The last time that i was able to get it start, i didn't turn on any power accessories (like headlights, A/C, stereo) and it was able to hold on till i drive it home (about a 10-minute ride).

Battery/starter seem fine because the engine cranks OK but just won't turnover. I have replaced the distributor cap/rotor, spark wires, spark plugs about 6 months ago. Before i replaced them, i was having problems starting the car on heavy rain/cold days (rare though). After that i think i had one or two start-up problems but if I keep trying, the car will eventually turn on. It's only recently the random shutoff problem become manifest (or is it because there's more rain in late NY summer?).

I have no idea about the condition of the alternator & fuel pump/filter. I don't think i have ever replaced them. Who supplies power for ignition while driving? Alternator or battery?

Oh by the way, on sunny days, 99% of the time the car is normal. There is only this one occasion that felt like mis-fires for about the first 15 minutes after i started it. Power delivery was intermittent; the car would jerk forward/not accelerate at all, when i press the accelerator. It only lasted for about 15 minutes though; after that, it was all fine.

This is all the symptoms that i could think of. There's this one post that i found similar to my problem and the guy said it's because of the ground wire issue (of the starter, if i remembered correctly).

Any comments/suggestions are welcomed. Help please. Thanks.