96 Jetta Trek, 2.0 gas. The car seems to have problems starting when it has been raining out. The engine is cranking OK from the starter (recently replaced) but it doesn't start for 5-10 mins of trying. Seems fine when it is dry out even when cold.

I've seen problems like this on other cars... is there a weak spot on this car (ie Dist cap) that I should seal up? Or replace?

The weak spot is the ignition coil. Do a search on this & you will find many with the same sputter or dies in the rain problem.

I agree with boschmann. I had the EXACT same problem with my 97 Jetta and when we tested the coil by spraying it with water it arced BAD. Had coil and coil wire replaced and that fixed THAT problem. Be prepared to spend some $$ on the coil.

I too have had problems with my Jetta when it was raining or snowing outside. The engine light would come on and the car would start to sputter, and would sometimes stall. I often had to wait a while before it would start again.
I replaced the disrtibutor, rotor, spark plugs and cables, and it only got better when I replaced the cables - and made sure to apply sufficient spark plug lubricant to seal the connection between the cable and the plug.
Replacing the cables without the lubricant was insufficient.
It has been a year and a half and I have not had anymore problems,

It was the coil after all... changed it and the car is fine now.

Thanks for the help.