SOLVED . . . re-selected data plan
Echoing the other users, I too had purchased two new iPad 3's yesterday and both of them had issues with activating the data plans. In particular, I'd initially entered my billing / account info, selected a plan, accepted the terms of service, only to have the data portion "stuck".
When I went to Settings > Cellular Data > View Account > Supplied Login Information, my account actually did populate with a Cellular Data Number as well as had issued to me the proper allotment of data when I viewed the "Current Plan Status". However, and this is during my 1st attempt at getting the data to function, when I'd attempt to browse/access the internet, I'd have an error thrown that said "no internet connection" (note: in the upper left corner of the iPad "Verizon" did appear with full bars).
To solve the problem, I did the following:
1.) Ensure that you have a Wi-Fi connection already set-up and active...thus providing an active internet connection (Settings > Wi-Fi > ON > then ensure a proper Network is accessible).
2.) You need to RE-select your data plan. Settings > Cellular Data > Cellular Data: ON > View Account > Enter your e-mail / password & click Next > Add Data or Change Plan > Select Appropriate Plan > Agree to All the Terms/Notices > You should finally have a "congratulations" window appear > Click Next.
3.) At this point I noticed that in the upper left of my iPad, the "Verizon" / bars disappeared and I instead had displayed "No Service". That is OK.
4.) Turn off your Wi-Fi. Settings > Wi-Fi > OFF.
5.) Open up a Safari page to see if the data plan activates & you have connectivity.
6.) For me, I actually did not get my internet connectivity on the Verizon network for roughly 5-minutes. That is, after doing all the above steps I just had to wait patiently for 5-min or so until, out-of-the-blue, the Verizon name & bars appeared in the upper left hand corner of my iPad.
7.) As noted in Step #6, my iPad 3 fortunately AUTO-provisioned the required connection from Verizon in about 5-minutes or so; however, I understand that if you were not as lucky as me, you'll need to manually re-provision your iPad. To do so, simply visit: Settings > Reset > Subscriber Services.
8.) NOTE: On my second iPad 3 that had the same exact issue, the only thing I did differently to resolve the problem was to use a unique e-mail address and a unique password (I tried the same pass but it actually required that I change it and create a new one).
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If you're curious as to the reason why this problem occurred in the first place, read on.
According to the Verizon engineer I spoke with at 888.294.6804, this issue occurred because during initial set-up my new iPad 3's, (and this is key) I selected the option for "Restore from iTunes Backup" (as opposed to the option for "Setup as New iPad"). When I did this, the settings from my old iPad 2 relating to Cellular Data transferred over to my new iPad 3. The problem is that my old iPad 2 was still powered on and the Cellular Data connection was still on (i.e., there was an active link from my old iPad to Verizon cellular network); thus, when my new iPad 3 was going through the initial set-up and was "restored" from my backup created on iTunes (or iCloud Backup for that matter), my new iPad 3 was attempting to access the Verizon network simultaneously using the same credentials as my old iPad.
Point is, the Verizon network detected two iPads attempting to connect using the same credentials so it automatically denied access to the newest connection attempt (my new iPad 3). The Verizon system was designed to clear out of the new iPad that erroneous 'old' account information and allow the user to simply create a new Cellular Data Connection, just like one would typically do if they were setting up a new clean iPad (i.e., a device that was not restored from a backup). Unfortunately, in practice, the system didn't operate quite as designed . . . what happened was that even though the new iPad device had its settings cleared out so that one could enter in their personal info/billing info; the back-end Verizon system still had fragments of those "old"/duplicate settings linked to the SIM card being used on the new iPad...hence the problem. So, as the above steps (#1-8) outlined, the only way to get the "problem" cleared out is to force the Verizon back-end to refresh & repopulate the billing side of the account (hence the reason why one needs to log-in to the account plan options, RE-select the plan desired, and then re-confirm all the notices and such).
Long story short, it seems that the Verizon billing back-end isn't able to 'refresh' as effectively & efficiently as the physical hardware side of the Verizon system . . . hence the reason why I was issued a new Cellular Data Number as well as a "plan" (i.e., the physical hardware validation checks all passed), but the system sort of froze / stuck in such a way that caused internet access to be denied (i.e., the billing back-end detected no payment being processed so it denied access to the data).