Well, I got a bit worried there...so I went to my graphics folder where I stash my things to use on the net and deleted an old smiley that I really don't need. It deleted okay, with right click.
I did it within a program, and not straight out of explorer. The site I read seems to imply that explorer.exe is the problem.

I wonder if you moved all the things you want to delete to a new folder, and then if you deleted the whole folder with a new name if that would work? Or have you tried that?

You know, explorer does not exist as such in Windows 7. I haven't gotten my head around that yet. The folders are different too. Hubby is slowly putting stuff back on the new machine, so I don't get to use it much yet. This new programing is obviously intentional!

Do you want me to copy/paste the second link for you here?
Avast didn't stop me, and our weekend scan didn't find anything.
That idea to boot in safe mode ..sounded interesting to me.
I'll call Kevin today... his office uses Windows and they might have encountered this problem. They log all the help desk actions and must delete sooner or later after some time, etc.
They just came out with a new software, and debugged it, so maybe they are good with debugging?

edit-- I just found this:
http://ask-leo.com/why_cant_i_delete_this_file.html
He goes on to recommend a program to fix this. --a Free Windows
program.

and here is another advice link:
http://winhlp.com/node/39
I have to confess I break out in a cold sweat and feel panic coming on with some of these suggestions...command lines, screen going black, etc!