SQL Server is not showing in Visual Studio

Had the same problem, after searching google for 2 hours while finding nothing, and the server name still wasn't there after refreshing for 100 times!

(server not working image)

Then, I tried 1 more thing:

Ignoring the fact that my server doesn't apear on the list.

I just wrote the server nae "(local)\SQLEXPRESS" and went to the connection name which now was enabled! (I didn't realized that before!)

if you were fools like me, this might be the answer!

(server working image)

If the SQL Server Browser service isn't running, it won't find it (which you have disabled). You should still be able to connect to it even though it isn't "discoverable". Try connecting with (local)\SQLEXPRESS.