** Who would I get in touch with about this problem? Is it a plumbing issue? **
The hole could likely be filled in by a general contractor or mason if you can't do it yourself. I don't know whom you'd call about the water build up in the well, maybe a landscaper or general contractor?
The vent itself by a general contractor (if you could find one with dryer experience) but an appliance service technician might be best if you can find one willing to do vent installations or alterations. Call around to some of the local appliance repair companies and ask if they could do it or can recommend someone.