Right. Let me try to be brief about this. First, the iPhone doesn’t seem to want to ever connect to YouTube when you’re using a wireless network. Safari, the web browser, works just fine, but not YouTube. As does everything else, as far as I know. So if you can’t get at YouTube, trying going through the regular (and slow) AT&T “EDGE” service.
Now, if it’s not even working through that, you can try two things. First, give the iPhone a hard boot by holding the power button on top down until you get the red “Power Off” slide on the front. Power off, and start it up again (you’ll see the Apple logo if you did it right).
The other option is to “restore” the phone in iTunes. It’s not as scary as it sounds. Everything will re-sync. Make sure you don’t restore to a backup; restore it from scratch. That oughtta work.
In the meantime, hopefully we’ll get an update that will let wireless networks work better with the iPhone YouTube option. Or perhaps some which is actually useful, like a Flash player for all that video you can’t see everywhere except YouTube. Thppthh.