Refer back to the posting by JustinC. Sounds a lot like the "SecureTempFolder" has gone stupid.
Rhyme or reason doesn't seem to fall into it. I had this one the other day. Now when you change the name of the folder make sure the full pathname is found. Also double check and make sure the user in question has full create access on this folder. You will also have restart the PC (not login logout) to make it work.
And it won't be all computers, it will work in OWA and not Outlook. You will also find "Save as" doesn't work for the same reason.
In Outlook 2003 (Don't remember prior versions for this) when you go to open an attachment, it creates a temporary copy in the secure temp folder (Hidden amongst temporary internet files physical location, so you can't NORMALLY view it unless you're a different user or cmd.exe prompt)
What you're viewing is a copy. If that folder can't be written to for whatever reason that will prevent you from opening attachments in Outlook.
Creating a new one in an alternate location via changing that key will alter things. I also found when I granted the user full rights to that folder it would autopurge entries from there as well. I think it's supposed to anyhow but I've found big piles of attachments buried in there that occasionally we need to purge when dealing with the Fax software on SBS 2003.
Well all else fails, make an offering to the computer gods. Preferably in small unmarked bills.