I don't think it's Avast asking you to pay. I think it's the program your mother downloaded and installed (by accident and unintended, no doubt). There are a lot of such programs, commonly called scareware or rogue; see http://en.wikipedia.org/wiki/Scareware for example.
How to get rid of it depends on what program it is. You didn't tell that. So please go to our malware forum http://forums.cnet.com/spyware-viruses-security-forum/ and make a new post with more details there.