problem with the restored database
What my colleagues are attempting to say in the comments, is that, they / we are making an assumption that the issue is due to the account / sql login not existing on your new server (the one where you restored your database). The most likely cause of what is going on is that since the login / sql account you use on your original server doesn't exist on the new server it's causing your application / connection to time out.

No biggie... easy fix with two options that come to mind to help resolve the issue. 

First option - Manually create a new user with the same name and password then run the following script on the database you restored:

sp_change_users_login 'update_one', '[yourDBuser]', '[yourSQLlogin]'


This will connect the newly created SQL Server login to the user in the database you are having issues with.

Second option (I prefer this one) - Install / create the sp_help_revlogin stored procedure on your original server. You can find the script here.

Once it's installed execute the following:

sp_help_revlogin '[yourSQLlogin]'


This will generate an output like so:

-- Login: yoursqllogin
CREATE LOGIN [yoursqllogin] WITH PASSWORD = 0x0200EF889B2ECBF4A17B836A62AE80BC0F718EBF117C73697892B112C3744D04AB18490E8C666C1154F42BC3D0C49346843032AFBFBEBA28CFE018AB1FED25EF2830A5F046E9 HASHED, SID = 0x01, DEFAULT_DATABASE = [master], CHECK_POLICY = ON, CHECK_EXPIRATION = OFF


Copy and paste the output onto your new server, and you will be rockin' and rollin' in no time.