A quick Google suggests that a possible fix may be this:
Caution: While these steps should be safe to perform if followed correctly, you should never edit the registry if you don't feel confident or are unsure of what you are doing.
1. Important! Close all Firefox, Opera and Internet Explorer windows.
2. Click Start > Run…
3. Type “regedit.exe” and press OK.
4. Get to the following location in the registry: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Windows
5. In the pane on the right-hand side of regedit you should see a String called “AppInit_DLLs”
6. Take note of any value listed to the right of “AppInit_DLLs” as it may indicate you have malware installed.
7. Right click on “AppInit_DLLs” and choose Delete.
Some application that uses a specific registry string, AppInit_DLLS at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Windows may cause the problem. There have been some reports that this string simply existing can cause the problem, without pointing to a specific application. The most commonly reported applications that this string points to are the pushow malware and Google Desktop. If the string points to a legitimate application, removing it might cause the application to stop working. Reinstalling the application afterwards may fix it, or it may recreate the string and the problem. Not everyone who has this string in their registry has a clipboard issue.
This information is extracted from http://kb.mozillazine.org/Clipboard_not_working
Use _At YOUR OWN RISK_