I've tried launching iTunes with quicktime open, yielding that semi-comical error message
Good to know. That suggests a weird issue with the %path% environmental variable.
Path contains a list of folders and the location of Quicktime is the last in the list. The problem is that if any of the folders can't be found, iTunes gives up and never reaches the location of Quicktime. (This can happen if, for example, a network drive has been specified in %path%, but you aren't connected to that network at present.)
If this is the problem you will need to edit the Path variable, but we need to know if this is necessary first.
In order to check this, type cmd into your Start menu search box and click cmd under Programs.
The command prompt window will open.
Type the following at the command prompt and press return:
cd my documents
This puts you in the (my) documents folder, next copy&paste the following into the cmd window and press return:
echo %path% >path.txt
This will place the contents of the %path% variable in a text file called Path in (My) Documents. You will need to check that each folder in the list actually exists.
In order to save time you can copy&paste each folder in the list into the address bar of Windows Explorer. You will get an error if the folder doesn't exist.
Make a note of any that don't exist and post back.