Have File On Desktop / Can't Delete

I have a file on my Desktop which I can't delete. It was a file downloaded from a popular video site using a download program. This program delivers the files that initially have no extensions. You then choose what format (ie. wmv, avi, etc) that you want your video file in. The program then creates a converted file with the extension you have selected. So you finally end up with two files. The orignal file with no extension, and the file that you have converted. Lastly you delete the original downloaded file that has no extension. This has worked fine countless times. But some sort of glitch occured with one of these files a while back. I was able to create the converted file without a problem, but I can't delete the original extensionless file. Whenever I try to delete it, I get a message that the file can't be read. So I seem to have a permanent unwanted file on my Desktop. Can somebody please tell my how I can get rid of it.