There is a large sticky in regards to "Software caused connection abort", however, since you didn't have this problem with your previous provider and your provider is the ONLY thing that you have changed, then the problem (to my knowledge) must be with the provider.
I know you said that they said they don't block, but experience has shown me that most of the people at the first level of help when you call an ISP actually have no idea about IRC or port blocking. You may need to call them back, then when you get to the first level help, ask for a supervisor or a more experienced technician.
