Whenever you bring up the task manager, is Explorer.exe running in the processes? If it's not go into File/new task(run) and type in explorer.exe and see if the desktop will appear again...even if for a short time.
OR....
Method 1
Step 1:
You may try to boot the computer in safe mode. Refer the following link.
Start your computer in safe mode
http://windows.microsoft.com/en-US/windows7/Start-your-computer-in-safe-mode
Step 2:
If this issue doesn’t occur in safe mode then you may perform a clean boot. Refer the following article.
How to troubleshoot a problem by performing a clean boot in Windows Vista or in Windows 7
http://support.microsoft.com/kb/929135
NOTE: Once you are done with clean boot, please follow step 7 in the article to set your computer back to normal startup.
Method 2:
You may try to perform SFC (System File Checker) scan on your computer and check. Refer the following article.
How to use the System File Checker tool to troubleshoot missing or corrupted system files on Windows Vista or on Windows 7
http://support.microsoft.com/kb/929833
Method 3:
I would also suggest you to scan your computer with Microsoft Safety Scanner, which would help you to get rid of viruses, spyware, and other malicious software.
The Microsoft Safety Scanner is a free downloadable security tool that provides on-demand scanning and helps remove viruses, spyware, and other malicious software. It works with your existing antivirus software.
http://www.microsoft.com/security/scanner/en-us/default.aspx
Note: Any data that are infected may only be cleaned by deleting the entire data, which means there is a potential for data loss.