It's generally advised on the Norton forums to run the Norton Removal Tool twice, just to be sure that everything's gone, although running it only once shouldn't cause the problems you've been experiencing.
Judging by the problems you're having downloading/installing and running various programs/applications, I think that it's very likely that you've picked up some malware somewhere. I suspect that bricat thinks the same which is why he wants you to post a log in the Hijack This Logs forum.
Is it possible for you to install the HJT file via another computer onto a flash drive and then install and run it on the affected PC? If not, I don't know what else to suggest and I fear your options will be somewhat limited.
You might like to have a look at the
AVG forum where you can read about installation/uninstallation issues, but I'm not confident that they'll help with your problem.