Always useful to mention operating system in your post.
One thing you can try is to disable them and re-enable from Desktop Properties. I'd also recommend trying to return them to their default icons as well.
To do this, find an open spot on your desktop (i.e. not over an icon) and right-click and select Properties from the menu.
Click on the Desktop tab at the top.
Click on "Customize Desktop" button at the bottom of that tab.
On the General tab (at the top) uncheck all 4 icons at the top (My Computer, My Documnts, etc.etc.) then click OK and OK..OK.. until back at the desktop. Verify you do not have these icons on your desktop now. If you do, they are simply shortcuts and you should delete them.
Now, repeat the above steps.. but this time re-check each of the four items, as well as visit the icon area in the middle and click "Restore Default" on each one. Then click OK, OK, OK.. all the way back to the desktop with your fingers crossed.
Start>Run then copy & paste or type in:
regsvr32 /i shell32
Note that the spacing is important.
It should,hopefully correct your problem.