Rain and moisture prevent car from starting

Hi all,
My 1997 Ford Aspire which I bought used with about 60K miles has always had a problem with rain and moisture. It would basically hesitate and not run smoothly during a rain or on damp days. Once warmed up it would be just fine. 4 years later, for the last 2 weeks the car will not even start. It cranks, I know the battery is strong but I have a hard time starting the car. I have succeeded in starting it last night. It was a dry, cold day and I drove the car for more than 30 minutes with no problems. It has been raining and it is very damp today and the car is in the garage not exposed to water. As I said I drove it last night with no trouble but now today once again the engine will not turn over. It's been a mystery. What can I do? As said before one day the car is fine and the next (damp, rainy day) it will not even start. I am consulting my priest for an excorcism but perhaps a more worldly solution does exist:)
Please help:)
Thanks