Many thanks to truenorth, patio and hartbeatmr and Allan. The advice given by patio to slave my HDD is frankly a little bit too comlicated for a novice such as myself. No virus was detected on my computer by Malwarebytes or Super antispyware. I have yet to try CCleaner Slim, AdwCleaner and DDS as per the help sheet by evilfantasy.
Alternatively, if somehow I can get my old PC online, I will try and register it that way and see what happens. Phoning Microsoft earlier did not solve my problem.
Is it possible to LAN connect my troublesome desktop PC with my laptop which is internet connected ? Would this method give my old PC the internet connection which I need ?