I hope I'm correct in this, but I've always believed that it would be normal for your iPad not to 'turn on' again after you use the "Erase All Contents & Settings" feature. You are basically wiping it and will have to start all over again as though it were in fact a NIB item, going through the initial setup procedures.
For me, still in the original iPad and with iOS 4.x running, that would mean not much happens unless and until I connect to a computer with iTunes installed, but whether that would also mean being stalled at that Apple logo display or not I simply don't know. It's been a long time since I set up this iPad and I can't recall what the screen may have looked like in the process.
Why you were unable to connect to iTunes is a bit of a mystery, of course, but probably has more to do with stuff external to the iPad than to the iPad itself. What that may have been would require more troubleshooting than you're probably willing to be doing at this stage.
Finally, I know that the setup process is somehow different for iOS 5, that you get some sort of Assistant popping up and can actually do it all wirelessly in some fashion. If that wasn't happening for you then that might be either a sign of a fault in the iPad somewhere or, also possible, simply a donut hole in the OS design that you happened to fall into, one in which the Assistant only comes to life the first time out of the box. I've only skimmed the User's Guide for that OS and can't recall seeing anything specific about that, nor recall having heard in discussed in the threads that I've looked into.
The main lesson, bottom line? You need to get a MacBook Air .....😉