Also my IP address was reported to the server I access my internet through as being abusive which I definitely was not and consequently I have received a verbal warning from the server ... They were also running my computer even when I was not using it somehow.
Whatever was going on in the background (when you weren't using the computer) is likely what got reported. They could have been using it for sending spam email, file sharing, any sort of activity they would want traced to somebody else. As HintOfLime said, it's likely that site wasn't the real culprit... their system could have been infected and controlled by somebody else, and passing it along to visitors.
Only if you can prove that their site is the one that infected your system (proving that is not easy!), report them to their ISP.