FIXED!!!! For me anyway, and I hope for you!
So I tried to update to ios 7 and after downloading the software itunes tried to update my iPad 3. I recieved the error 3004 and was stuck in the "Connect to iTunes" screen and
could not get out of it. Completely annoyed!
But then I remembered something from when I used to fiddle with iphones. I opened a program I had called TinyUmbrella, which can be used to force boot out of recovery mode (the
"connect to itunes" screen).
My ipad was still connected to itunes and in recovery mode. I opened TinyUmbrella, selected my ipad (which was just shown by the serial number), then clicked "Exit Recovery" and
BAM!!! It immediately kicked my out of the recovery screen and started my ipad back up to my home screen.
Now, my ipad was still on 6.1.3 since the update to ios 7 had failed. But I didn't care, my ipad was fully functional again just like I left it before. Thank God for
TinyUmbrella! Here's the CNET link for TinyUmbrella if you need it: