I am assuming you are using the minecraft browser?
So going off off that, you can download a client that is called WoM and XWoM.
First you will need to download the WoM client at the worldofminecraft.com webpage. I believe you need to make an account there first, but no big deal.
Then just google XWoM client, I can't remember the link, and download XWoM. What you want to do now is extract the XWoM application and put it into your WoM Folder.
Then just run the XWoM client and provide your minecraft log in details and a server list should pop up.
This will provide you with a full screen version of minecraft classic, and provides some useful tools. Have fun!
If you want to continue playing on the browser, I would say just try another internet client.
If it is the account that is the issue. Go to the Mojang website and file a report with them, they will sort it out.