Cannot connect to SQL Server database regardless of connection string
If you have access to SQL Server Management Studio, then attempt a logon to MIKE-LAPTOP with your provided credentials.  Can you connect?  Any errors thrown?  That will eliminate the possibility of password/permissions.  

You mentioned that there could be multiple SQL instances.  Depending on configurations, you may need to specify the instance name and/or port number.

Such as:

MIKE-LAPTOP\sql2008 
MIKE-LAPTOP\sql2008,1433