That error is usually an error for an account that wasn't setup completely when you first went to set it up. I had the same problem. I had to completely re-register. Their tech support had to go in and unlock the username so that I could use it.
Here's a description of the facts (and the time spent, so that you can get a basis if you have this same problem):
02/28/2011: I've created my Magic Online account (with an email account from Yahoo.com.br). Payed by PayPal. Waited for activation mail that was not received.
03/02/2011: Tired of waiting for the activation mail, I wrote an email to Wizards of the Coast's Customer Service. On the same day they replied asking for all my information to prove that I was in fact the owner of that account. I gave them the information.
03/03/2011: WotC answered that they had "manually activated" my Magic Online account, and that any problems should be fixed, letting me log in with my username and password, adding that soon I would receive my starter packs. I tried to log in but keeping receiving the message "Error L0023: Unable to connect to the Magic Online server".
03/04/2011: I replied to Customer Service again, telling them of this error, and that I couldn't log in into my Magic Online account.
03/07/2011: Customer Service answered me that my "New Account starter pack" had "just been added to my collection and activated account" (...). I suceeded in logging into my Magic Online account.
So you see, since they claimed (on 03/03) they had already activated my account, maybe this error kept coming up because they had not yet gave me the starter packs of my account, and so I was trying to connect into an "empty" account. This was the explanation that I could get out of this whole week of (forced) pacience...
Gladly all is working fine now.
I hope this can help any other person too.
(P.S.: I'm not used to the tools of the forum so... How do I send a PM to the other threadstarters?)
That error message can also be due to your account being closed. This just happened to me this past weekend. My account was closed because Paypal did a chargeback without me knowing about it. Some security measure crap. Check your Paypal or bank account and make sure you don't have a charge back of any kind to them. The process to get it back sucks so I hope that's not it for your sake.