Sometimes it does. Sometimes it don't.

I have a 1989 gmc jimmy s-15 4x4 with a 2.8 v-6 5- speed std. It has 170,448 miles. On rainy days the check engine light comes on for a little while. I was driving in the rain and when I turned it off and then tried to re-start it it would not start. I was getting a weak spark so I replaced the coil but it still would not start. The next day it started right up and ran fine. But it would not start after I turned it off. I pulled a few plugs and it wasn't flooded. I have spark and fuel but no start. Also, my starter does not always kick on when I turn the key now. I was able to use a screwdriver on the solenoid to turn it over but now that doesn't work. It has never done any of this before. Could this be caused by a bad battery? If not what could it be?