Sigh.  Had ANOTHER problem with Battlefield 3 recently.  More annoyance than problem, but the icon in the tray for the Origin client was showing up as a busted link:

The Origin program worked fine, but it was annoying because sometimes I forgot I’d opened it and having the ‘broken icon’ button on your toolbar isn’t exactly helpful for finding it.  I tried right-click setting properties.  Changing the icon to a different icon then back.  Removing the program and re-pinning it.  Nothing worked.

Then I found this link.  Basically, you need to destroy and then rebuild/repair your icon cache.  You do this via:

1. kill explorer.exe
   taskkill /IM explorer.exe /F
2. Deleting your icon cache files:
   del %userpofile%\AppData\Local\IconCache.db /a
3. Reboot
   shutdown /R /f /t 00

Upon restart, your entire icon cache will get rebuilt (which could take awhile).  Mine took about 2-3 minutes during which the machine was almost unresponsive.  After that the icons re-appeared and all was well.

Link to script that does all this for you and further information.