All I can say is that I have done this many times and it should work.
If you want to use Filestream you will need to install KB 937444, but otherwise the SQL Enterprise media should have all the components you need to install on Windows 2003.
Sometimes the install will fail on a very slow server but this is normally shown in service start failures or non-existant paths in the error messages. Your problem seems to be a simple install issue.
You say you have reinstalled Windows. Is it worth getting a new copy of the SQL install media in case what you have is corrupted.
Original author: https://github.com/SQL-FineBuild/Common/wiki/ 1-click install and best practice configuration of SQL Server 2019, 2017 2016, 2014, 2012, 2008 R2, 2008 and 2005.
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