Can't connect to SQL Server 2014 Express

First off, open services.msc and scroll down to SQL Server, and ensure its started.

If its not running modify to start automatically, and then start it.

Once it's running, close services panel, and run ssms.exe (management studio) and try connecting to Server Name: <machinename> or Server Name: <machinename\sql2014> [no <>]. You can also click the Server Name drop down list, and select BROWSE to see if your instance is listed - although I find this hit and miss.

Once you confirm its active and you are connected, follow this msdn page and follow the steps to enable tcp/ip connections.

From there you should have the details necessary to alter your connection string.

SQL Server Express does not have TCP/IP connections enabled by default, instead it uses Shared Memory which means that external/remote connections from another computer won't work.

Open SQL Server Configuration Manager (it's on your Start Menu) and choose Server configuration and enable TCP/IP. Also open the properties for TCP/IP and ensure you have both "Active" and "Enabled" set to True on the bindings you want to use.