it said that the current QT was on a network that wasn't available to me and it wouldn't let me uninstall it so I got rid of the whole folder
Unfortunately, this sort of trouble has gotten more complicated to deal with ever since Microsoft pulled the Windows Installer CleanUp utility from their Download Center. First we have to find a copy of the utility.
Let's try Googling. (Best not to use Bing, I think.) Look for a working download site for at least version 3.0 of the Windows Installer CleanUp utility. (The results from mydigitallife and Major Geeks are worth checking.)
After downloading the utility installer file (msicuu2.exe), scan the file for malware, just in case. (I use the free version of Malwarebytes AntiMalware to do single-file scans for that.)
If the file is clean, to install the utility, doubleclick the msicuu2.exe file you've downloaded.
Now run the utility ("Start > All Programs > Windows Install Clean Up"). In the list of programs that appears in CleanUp, select any QuickTime entries and click "Remove".
Quit out of CleanUp. Restart the PC, and try another install. Does it go through properly this time?