This isn't legal advice, I'm just giving you some info, and a bit of my understanding. Check out
http://www.copyright.gov/circs/circ1.html#wci
"Copyright protection subsists from the time the work is created in fixed form. The copyright in the work of authorship immediately becomes the property of the author who created the work. Only the author or those deriving their rights through the author can rightfully claim copyright."
You get copyright immediately, you don't have to register.
"The use of a copyright notice is no longer required under U. S. law, although it is often beneficial."
Even though Neopets requires that you don't put the copyright notice on your artwork, it doesn't matter. You aren't required to in order to secure your copyright anyhow.
"Any or all of the copyright owner's exclusive rights or any subdivision of those rights may be transferred, but the transfer of exclusive rights is not valid unless that transfer is in writing and signed by the owner of the rights conveyed or such owner's duly authorized agent."
Neopets doesn't get your copyright unless you both sign something in writing. As far as I can figure, you've granted them use of your work. You still own your work and retain copyright.
Edited to Add: And I can't even figure out what exactly you grant them, other than maybe the right to display in the gallery, despite what they claim. Just because a clause is in a document doesn't make it legal. And if it isn't legal, that particular clause in invalid. It doesn't nullify the whole document, though. ...it's too complicated. Don't submit unless they stop claiming all rights from now until the end of time in all the universe.
