What is your OS ?
Firstly having two resident scanner installed at the same time can cause conflict and actually leave you vulnerable and Norton would appear to be worse than most when it comes to conflicting with other programs.
So the scanning issue could be a symptom of that conflict as avast opens a file Norton buts in and also tries to scan the file avast wants as they each try to lock the file to scan it. You really have to decide on which AV to have installed and uninstall the other, reboot, uninstall the one you want to keep, reboot and install it again.
You appear to have some form of spambot installed on your system.
If you haven't already got this software (freeware), download, install, update and run it, preferably in safe mode.
Ewido Security Suite If using winXP. or
a-Squared free if using win9x/ME.