Desktop was locked up. Clicking on icons had no action. Taskbar worked

Glad you fixed. One of those pictures has something bad in it. It could also fooled around with system files, that why I suggested running sfc /scannow. If you do run it more than once boot after each time.

I've run into this issue with a few friends, and now myself in 2016. I feel a responsibility to address this for anyone else searching for locked Desktop icons solutions for Windows 7. This thread is almost 5 years old and I have never yet seen any solution other than the below .reg files, taking a peak at the users registry path or re-booting and/or re-starting Explorer.

After the malware is taken care of, running sfc /scannow in Safe Mode with Command Prompt as Administrator will do the best job because the system is running with the least amount of locked files in use. Files that are protected and not critical to restart Windows are not repaired. When a file IS repaired the related registry keys are also repaired but, our mileage of course may vary. Layback Bear's excellent advice on re-booting after each sfc /scannow pass is crucial for the best repair.

Various times I have seen the users Desktop registry key get changed to another location. Drill down to:

HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders

Then check in the right column under the Name heading for Desktop
Scan to the right and make sure the Type heading for Desktop is REG_SZ like all the rest of course.
Then in the last column: Data - you may find the users Desktop path askew.
Make sure the path shows:

C:\Users\THE CURRENT USERS ACTUAL NAME HERE\Desktop

Where the underlined words in gray of course are the actual users name.
If you're at your wits end you can try this fix posted here on sevenforums at entry #8:
http://tinyurl.com/zzuu993
DO NOT click entry #8's url - it is a techjawa page gone malicious.

Here it is in the wayback machine:
http://tinyurl.com/zqsomxv
There are both 32 and 64 bit .reg files. Tested it extensively on a virtual machine 1st and then myself and others who actually had some of these strange issues.
Hope this helps :)