Here's how to uninstall 2013, reinstall 2012, free
I too was a many-year happy user of AVG Free, then experienced complete malfunction of the 2013 update--froze every time it tried a scan, things started disappearing from my desktop, etc. I read the many, many complaints and solutions out there, and here's what worked for me. It did not require any help. Hope it works for you.
Try uninstalling 2013 using this link: http://www.avg.com/ww-en/utilities.
Then reinstall one of the earlier versions with which you were happy, using this link: http://www.filehippo.com/download_avg_antivirus_32/12831/.
When you do the 2012 reinstall, be sure NOT to click on the upper LEFT green button, which will just download the 2013 update. Rather, look at the list of old versions of the program at the right, make sure it's highlighting the version you want, and click the upper RIGHT button that says "download this version."
You'll still have to deal with the 2012 version constantly requesting to be updated, and at some point it will probably tell you it isn't supported any more. Let's HOPE that by then the folks at AVG will have seen reason and fixed 2013.