In case it helps anyone...

I went through all the same endless loops about changing database permissions etc (for an install of 4.8.2) and had the same results. I finally found the solution for my installation in a completely separate area, FILE PERMISSIONS.

At the inital DNN setup stage it had told me I needed to set file permissions properly (because everything was read only) - I experimented with what it needed to get past this stage; adding ASPNET write permissions didn't work but adding IUSR_MACHINENAME write permissions did. So I removed the ASPNET permission and carried on with the wizard.

While trying to fix the DB not installing problem, I noticed that the web.config did not seem to be being updated. The fix to this was to add back the ASPNET write permissions *as well* as the IUSR_MACHINENAME. once I'd done this, the database installed correctly. I guess this is why a workaround is to manually set up the connection strings in the web.config.