What version of windows are you running?
Now I'm not on my home PC and my work PC is locked down pretty hardcore so my walkthrough will be hazy but...
Right click on the file and go to Properties.
There should be a security tab. Click it.
Go to the advanced security settings and remove all the users from the permissions list.
Add the user definition "Everyone" and give full control.
Then try to delete.
Again this kind of depends on the OS you're using as my XP Skizzillz have become dull. Here
's a walkthrough if you're using XP on how to take ownership of a file/folder. After you have ownership, just delete it.
If the above steps do not work, boot into Safe Mode under the administator account and navigate to the desktop folder of that user and delete the file.
If you're still unable to delete it, then my next thought would be malware. Get Malwarebytes, install, update then scan and see that comes up with anything.