Hi Dan - And welcome to the forum.

How long has this been happening?
Do the icons remain unmovable after a reboot?
Are they responding at all, can you click on them to run a program?
Have you installed anything new of late, any new software or maybe a browser plug-in or add-on?
What browser are you using?
If you start the computer in Safe Mode, can you then move the desktop icons?

I suspect maybe a software conflict or corrupt file. Please answer the questions above and we'll take it from there.
Cheers... Jim