I hope for help
I see nothing bad in your HJT log.
Can you describe the problems you've been having?
Internet is very slow on a particular website
My internet connection is very very slow to this site:
Where it is fast elsewhere.
I don't know why it is slow to that site, although I doubt it is a malware problem.
TechSpot's member Jobeard knows a lot about problems like this; perhaps you could PM him.