** how do I go about closing up the existing vent hole? **
If the vent went through a concrete or block wall, the hole through it could probably filled in with a concrete patch and the existing ducting *totally* removed so there is no mold growth possibility.
In regard to the original problem, if it is impossible to install a proper vent, maybe you could considering purchasing a ventless dryer that is designed to operate without an out side vent? They're a bit pricy though (see the following link).