One question, does your new server have a graphics library? Mainly GD2 (which at the moment is the default library base). Capcha also uses that as well. Also in Registration basic options ensure that GD2 is turned on (by default you have two choices, disabled and use gd2)... I know you may have already checked this but as nothing else has worked I would recommend a second look into this to see if it helps at least.
Dunny