Updating SQL 2012 SP1 to SP4

You might not have selected the right SQL instance?

Can you run the Services app and show us what it says for entries starting with ‘SQL Server (MSSQLSERVER)’ ?
You can also run the ‘SQL Server Configuration Manager’ and show us those entries under ‘SQL Server Services’.

If a named instance is installed, it will show up as 

‘SQL Server (<INSTNAME>)’.

Can you also run SSMS and connect to that instance, and show us the version number ?
SQL 2012 SP4 should be 11.0.7001 or higher.

You are running the Service Pack update directly on the SQL Server machine, yes?
It would have created a summary text file report at the end; did you look at that text file report?

Similar to ‘C:\Program Files\Microsoft SQL Server\110\Setup Bootstrap\Log\Summary.txt’