I've just noticed an odd problem with Quicktime. When I click on the app to open, it literally opens the desktop folder and not the Quicktime app. Furthermore, when I try to play a file through Quicktime it says that Quicktime cannot be opened. Essentially, I can't access Quicktime at all.
Does anyone have any idea as to why this may be happening?
Your question/issue description is somewhat ambiguous.
If you mean that when you double-click the QT X v10.4 Player icon a "Finder" window automatically opens, then it sounds as if everything is operating normally. That is, the application opens, sees that that you did not double-click a specific media file to be opened or don't have System Preferences set to automatically re-open any previously opened files in player windows, and, therefore, automatically opens a Finder ("Open File") window to allow you to navigate to/select a specific media file to be opened. (I.e., this is the default workflow for many Apple apps under the latest Mac operating systems.) In this case you can either double-click QT X compatible media files in the Finder to open them immediately in a QT X player window or turn off the System Preference in the "General" widow that closes currently open files when apps like QT X, Safari, Text Edit, etc. are closed/quit by the user.
On the other hand, if you mean something else here, please describe both your actions and their results in detail. It is possible that the the QT X Player and/or your operating system have become corrupted and might need to be re-installed.
