I asked some questions, these are to try and clarify your issue and I'm still confused as the questions either weren't answered or not in detail.
You keep talking about Programs and I don't what/where you mean when talking about that ?
The same when you talk of Downloads, where is that ?
The major one being is avast listed in the Control Panel > Programs and Features list of programs ?
If not it makes things more complex as it is an indication that you may have a corrupt installation..
Essentially you can't move the installation from one place to another, you will have to uninstall it from its current location and reinstall it in the default location.
Note: avast allows for installation in a location of your choice (there are exceptions, link not on a removable/external hard disk) and it should still work. If the remainder of avast is working in this 'Downloads (?)' location then so too should the firewall. So there is likely to be something else going on.