Alright, guessing that your Server Name is indeed correct here what to do...
Start->Run->Type "msconfig" (without the "s of course)
OR
Press and HOLD Super (Windows) key then press R, Type: "msconfig" (without the "s of course)
A window titled "System Configuration Utility" should come up.
Along the top there should be some tabs, one is labeled "Services", click it.
Look for a "SQL Server (SQLEXPRESS)" is the box next to it checked? If not then check it, now the SQL server will start on startup of computer.
If you do not want it to start at startup follow this:
Start->Run->Type "services.msc" (without the "s)
OR
Press and HOLD Super (Windows) key then press R, Type: "services.msc" (without the "s)
A windows titled "Services" should come up.
Scroll on down to: "SQL Server (SQLEXPRESS)"
After you click it in the information side bar you should be able to Start it (if it is not started) if it is started then you should be able to restart, stop, and pause it.
If there is no start option it is either disabled or already started. If it is disabled right click "SQL Server (SQLEXPRESS)" and go to Properties, as the Startup type select what you want (I have Automatic) you can choose manual if you want, you just have to start it everytime you reboot. Now you should be able to start it, try logging in now.