I've stopped using twitter myself due to the fact they've locked me out when I didn't give them a phone number. As far as I can tell, that's the only reason they've locked my account.
Yeah, that's annoying, a lot of new accounts get locked instantly and asked to provide a phone number. Technically you can appeal it, but you have a lower chance of being accepted now than in the past. However, you can use Google Voice, or a site like getsmscode.com (that one is confirmed working on Twitter, just sometimes a bit flaky, may have to try multiple numbers).
