If the SQL install stops when installing the Setup files, typically this is because one of the pre-requisite components has not been installed. Unfortunately just about the only clue you get about this problem is an absence of installation logs, so it can be difficult to troubleshoot.
Check what versions of .Net, Powershell, and Windows Installer are needed, and make sure they are installed before you run the SQL Express install. For SQL 2012 express you need:
Windows installer 4.5
Note that .Net 3.5 and .Net 4.0 must both be installed, 4.0 does not include the 3.5 components. You should also run the installs in the sequence listed as the pre-reqs also have their own pre-reqs.
Original author: SQL Server FineBuild 1-click install and best practice configuration of SQL Server 2017 2016, 2014, 2012, 2008 R2, 2008 and 2005. 1 Dec 2016
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Disclaimer: All information provided is a personal opinion that may not match reality.
Quote: "When I give food to the poor they call me a saint. When I ask why they are poor they call me a communist." - Archbishop Hélder Câmara