95 Cabrio- Multi faceted start problem

[violaguy]

Have the problem of damp weather (rain or humidity) making it VERY difficult to start. It eventually WILL start, but sometimes I have to repeatedly crank for up to 15 minutes before it'll fire up.

More recently, I've noticed a strange whining noise, almost like a dental drill, when I turn the key. This happens, but the starter doesn't seem to crank during the whining noise. Then, after a few attempts, the starter turns enough to start the car.

When the car is being started for the first time in the morning, the whining noise doesn't happen. But, if I drive for awhile, turn the car off and then restart (like going to the store for a brief period) the whining noise is really bad, and it sometimes refuses to start altogether....unless I wait a couple of hours. Then it starts normally.

I have a 95 Cabrio with 150k miles, manual trans.

Sound familiar to anyone?