Okay I finally found the solution to a problem I've been having for almost 2 months. Here is the summary of the problem, cause and fix.
How to Fix Microsoft Word 2010 Icon
Problem: Microsoft Word 2010 application icon not showing up properly, instead a broken icon is displayed.
Cause: Installing Microsoft Service Pack 3 can cause glitches in some icons (not just MS Word 2010) not displaying properly.
Fix: Go to Control Panel -> Programs and Features -> MS Office 2010. Right-click MS Office 2010 and select Change (DO NOT UNINSTALL!). Select Repair in the next pop-up. Wait a few minutes (shouldn't be longer than 3 minutes). Accept the system restart pop-up. Restart the system and the icons are now back to normal.