Hmm, I think you are best to only run Construct Classic (and whatever graphics programs you need) at the same time, and then close Construct Classic when you go to use Chrome or something else.
The other issues your computer is having is probably not specific to Construct Classic, but just when it tries to run other programs at the same time.
I would suggest only re-installing Construct Classic, as the other things should never be affected or have an effect on each other. Please try re-installing Construct Classic R2 (from the link I posted a few days ago), and make sure it is installed by using Right-Click > Run As Administrator to be sure it's working properly.