Finally, problem solved. I booted in Safe Mode and did all that zilto suggested. It didn't help me but it gave me something to think about.
I looked at the extensions and went to search. I typed it in and it gave me a ton of them. Then, I tried to delete them from the search. It would not let me....my thought, because there were too many. So, I did it again but stopped the search quickly. Then I was able to delete 4,670 files from the desktop. I did the same again and was able to delete another 4,675 files.
I went back to desktop and looked for more extentions. There was one extention left. Then I did the same with that extention and deleted them from the search. A total of 630 files were deleted. I am keeping them in my recycle bin until I have decided, that nothing on my computer was affected by their deletions.
Thanks for all of the answers. Sometimes, we need to run things in front of others to get our own minds to working. I could not have done it without all of y'alls input. Thank you so much as now I have a clean desktop. Yeah.....