AV programs have huge resource footprints, so even when they're not scanning anything, they're still using a lot of memory. Compliment this with older laptops, and it's no surprise that your system slows down.
Avast, in my experience, has caused more problems than it claims to fix. If you can't find any removal tools for your Avast AV software, download and install Smarty Uninstall. You can use the free trial for 30 days and in the mean time remove all traces of unwanted software (because Add/Remove Programs doesn't remove software completely).