It honestly sounds like you're at the stage where you need to ask more questions.
Do your statistics suggest that a large number of people start the old version of your form but fail to complete it? That might indicate boredom or insufficient incentive to get through a boring task. While novelty (such as a cube interface) may help, you might have more success by reducing the form's length. If this is a crucial form that people are forced to complete, then you should error on the side of boring but impossible to be confused by (i.e. not a cube).
Do people tend to have the highest probability of quitting at a small number of specific questions? (e.g. Hi. We'd like you to participate in an anonymous survey! Q1: What is your social security number?) That might indicate something else, like one of the pieces of information your form requests is something users are uncomfortable sharing. If this is the case, a spinning cube is definitely not the answer.
Ask questions like the above, and then ask yourself how the cube interface addresses them. If all it does is "be novel" then you may have a problem. One person's novel is another person's confusing.
Personally, I'm having a hard time coming up with how a cube interface really adds anything meaningful to the process of filling out a form other than adding eye-candy. Filling out a form is a linear process. How does associating different fields of the form with the sides of a 3D object help the user fill out the form? Could having adjacent fields on different cube faces actually get in the way?
Again, if all the cube interface does is "be less boring" then I think you should really look at alternatives. Spice up the language of the form. Instead of "address" put "Place where you want us to send spam printed on genuine dead trees!" (This might be off-putting if you are actually a spammer!). Try adding fun stuff. e.g. Right after name, add a field for "secret agent call-sign" (Possibly useful for password recovery). Play with the typography and interface. Make the form pleasant to look at. (I know the cube picture Roger posted above is just a quick and dirty mock-up, but if you think it looks remotely close to finished form you probably need to get help with this.)