Welcome to the forums, Wenzz!
What anti-virus, if any, did you have on your computer before trying to install avast? Some are difficult to install completely and require more than 'Add/Remove Programs.'
Did you try to download and install in one step? It might be better to download and save to your hard disk (you desktop is a convenient place) and then run the file you saved.
Which site(s) did you download from? I would suggest downloading directly from the avast! website, rather than from download.com (click on screenshot to enlarge).
By the way, I also have a computer running WinME, and have been using avast! home on that computer for more than a year.