As others suggested there could be scores of things went wrong which cause this problem. I would suggest you to read the suggestion given in the following post to start investigating your problem:
Webrole is not starting and always busy
Here is the connection string you would need to add into web.config to connect SQL Azure DB from ASP.NET application
<connectionStrings>
<add name="SQLAzureConnection" connectionString="Data Source=<ProvideServerName>.database.windows.net;Initial Catalog=TestDb;User ID=<ProvideUserName>;Password=<ProvidePassword>;Encrypt=true;Trusted_Connection=false;"
providerName="System.Data.SqlClient" />
</connectionStrings>
