I have a Macbook Pro (Mac OS X 10.5.8) and every time I try to download Quicktime it won't work. It downloads the dmg file, runs the program fully and then, finally, asks me to restart my computer to complete the download. Once my computer restarts, the program is no where to be found on its hard drive...

I don't know what to do. I would love some help because repeating this obviously isn't getting me anywhere...

First, are you downloading it through Apple's web site or through the Software Update on your Mac? If one doesn't work, try the other. Also, you might be able to do a work around. If you go to Apple's website, you can download both iTunes and Quicktime together. That installer may do the trick.