1992 Acura Integra

I have a 1992 Integra, 170,000miles, 1.8 liter, automatic trans.
I have a problem that seems to happen when its hot and humid out, about 85 or hotter. When I go to start the car, it will crank but there will be no spark to the engine, whats more is that in the cluster, where it goes from park, reverse, neutral, drive, sport3/4, and 2 the S3 light will blink. I tried to count the blinks but it just blinks for as long as the key is in and turned on. If I wait for ten minutes, i'd say half the time that it will then start. I worked in a parts store this summer so I got some stuff that I thought would solve my problem, my car has a new coil, rotor, distributer cap, wires, and fairly new spark plugs. Another problem that I have is one that occurs only when it is cold out, aka winter. The problem with that is that I am from Buffalo, Im currently at school in New Jersey, but it still gets cold here. Anyways when the car is cold, and I go to put it in park, the car doesn't recognize the fact that the car is in park. This is a problem because I 1. Cannot get the key out and 2. If I need to get back in and go somewhere I can't get the car into gear.
I would also like to add that I'm a poor college student operating on a very limited budget and may be doing the repairs myself if they are within reason.
thanks.