If you're savvy with that IVR sometimes when it errors out it will transfer you to a port center rep.
Also, just make sure that all the information you're giving the new service provider is correct. Typically they'll need your phone number, account number and password. They also need to know the account owner's name and billing address. Double check that stuff to make sure it's correct.
Otherwise I would just call VZW CS directly. Ask them what's up with your account. If needed they can transfer you directly to a live person in the port center and they can check it out.
I'm surprised that your new service provider didn't have it's own port center, or if that's who you talked I'm surprised they weren't able to tell you what's wrong.
VZW outsources it's port center reps to a center in Oregon, mostly, and they're always extremely knowledgeable. Their tier 2 reps are especially savvy with the whole porting process and the typical problems that come up.