Val, I'm assuming that you're running Windows XP and that those desktop icons are shortcuts. Go to the link below, click on Win XP Fixes, click on File Association Fixes, the download the ''LNK (Shortcut) File Association Fix'' which is a .zip file. Download the ZIP and open it. Extract the REG file to your hard disk and double click it. Answer yes to the import prompt.
I've seen this message before but the answer escapes me. My desktop icons won't open any programs unless I right click and then open.