It will be for ever impossible for Windows Movie Maker to open Quicktime files. Windows is from Microsoft, Quicktime is from Mac. They both think they're the best, so naturally they hate each other.
What you will need is a tool to convert these Quicktime movies into something that Windows Movie Maker can understand, namely the Windows Movie Format (WMF).
There are a zillion of converters tools on the internet. Some are good, most are not. Some are easy, most are not. I suggest researching.. a lot.
I like the VLC media player (www.videolan.org), since it can play almost any format (so both WMF and Quicktime) and convert it as well without too much hassle.
I recommend reading this article about VLC if you are interested in VLC.