Hello minerva and welcome to the forum.
First, I would uninstall ad-aware since this is an obsolete program that has now been replaced with better definitions with Malwarebytes (MBAM). Upon uninstalling, use the vendor's uninstaller tool, then
reboot your machine.
After this, use a cleaner like CCleaner, freeware system optimization, privacy and cleaning tool. There is a
Slim version available as well at
http://www.piriform.com/ccleaner/builds – 4th option down. It removes unused files (cache, temporary Internet files, etc.) from your system, allowing Windows to run faster and freeing up valuable hard disk space. It also cleans traces of your online activities such as your Internet history. Additionally it contains a fully featured registry cleaner (make a backup in Documents as a just in case). Reboot.
Next, reinstall MBAM
http://www.malwarebytes.org/, make sure you update both the program to 1.50.1.1100 and update the definitions. You need to update the definitions prior to scanning every time. Run a full scan (in the future you can run a quick scan) and make sure you put any infections into quarantine. Report back with a cut and paste your MBAM report from the log tab of MBAM so we can analyze.
When you did your uninstall/reinstall of Avast the other day, did you use the Avast uninstaller tool
http://www.avast.com/uninstall-utility?
What firewall do you use and does it allow Avast permission to access?
Please let report back with your MBAM log and let us know if any of the above helps fix your problems. Thank you.