What I want to do is reinstall Avast without having to pay for it. How would I do this?
you did save your license file?

run this first. http://www.avast.com/uninstall-utility
download and install your program. http://www.avast.com/download-software

insert license file
https://support3.avast.com/index.php?languageid=1&group=eng&_m=knowledgebase&_a=viewarticle&kbarticleid=1084