Hello tathraman and welcome to Seven Forums. Some things you could check:
1. Do your desktop icons appear under C:\Users\%USERPROFILE%\Desktop? If "yes", copy the files to the desktop.
2. Several internet searches for missing icons show that a 3rd party software called InfraRecorder is set by default to not show the icons. If you're using this software it might be to blame.
3. You could try rebuilding your icon cache and restoring default icons to your folders.
Icon Cache - Rebuild User Folders - Restore Default Icon
4. You could also see this tutorial for gadgets if they're also affected:
Gadgets - Turn On or Off
5. And if you changed your theme, especially to a 3rd party theme, that could affect if your icons appear or not.
Theme - Change or Save
6. You could try to right click desktop > view > show desktop items or right click desktop > personalization > change desktop icons > restore default > ok.
7. I also think I remember reading that if User Account Control is turned off there can be issues with gadgets showing and customizing folder icons. If this is also an issue you might check if UAC is turned off. If it is, try using the least invasive setting.
User Account Control - UAC - Change Notification Settings
Appreciate it if you'd post back to let us know if anything helped or not. Others with similar problems could benefit from your results.