macOS Sierra 10.12 not installing

Hi Guys

I made the mistake of buying a late 2013 27" iMac as a second computer for home use. (Late 2013 3.2 GHz intel core i5)

The computer runs on os Yosemite, but what I did not realise at the time of the purchase is that there are issues to update to later OS versions.

I did a factory reset, but nothing works. Safari does not allow me to login to the iTunes store - says password is incorrect + Safari also says that a secure connection cannot be established with Apple.com - go figure that - how is that even possible??

However, according to my research, this iMac can be upgraded to some later versions so that it can actually be used for something other than a paper weight.

I also did all the steps to check for certificates, DNS, IP address, etc - still nothing.

I then downloaded Sierra 10.12 from Apple support via the Chrome browser - installed it successfully (well according to the installer at least) - restarted the computer - still Yosemite. My thinking was that if I could install Sierra 10.12 Safari/Chrome/Firefox browsers would actually work and then maybe I could proceed to install to the latest possible os version that can run on this computer - no go :-(

Just don't know what to do next - please put me out of my misery and advise me how to get this freaking computer updated to a later os version so that I can actually use it.

All the tech we as a family own is Apple, and I am really disappointed that I am struggling with this issue - all my other devices just work with no issues - was expecting the same with this computer.

Cheers

D

PS - this message is sent from my other iMac - 2014 version that works just fine and runs on the latest os version, because my "new" 2013 iMac paper weight does not allow me to do anything.