Please, answer first these questions:
What version of Windows are you on? Is it 32-bit or 64-bit?
Go to Windows Start and in the Search box type winver.exe and then press Enter.
What is the version of Internet Explorer installed on your computer?
In Internet Explorer go to Help -> About Internet Explorer.
P.S. Please, don’t say that you are not using Internet Explorer. This is irrelevant. Skype depends on Internet Explorer.
Here are ruwim's suggestions for correcting your problem:
Go to Windows Start -> All Programs -> Accessories -> Right click on Command Prompt, select 'Run as administrator'.
The Command Prompt window should show:
If this is not the case, then at the Command Prompt type: cd c:\windows\SysWoW64 and press Enter.
Once you see C:\Windows\SysWoW64>
Type this and then press Enter:
Next type this and press Enter:
After each Enter you should receive a message saying that DllRegisterServer in XXX.dll succeeded.
Reboot your computer.
Open in your Internet Explorer (no other browser but only IE 32-bit version) this page:
Click on the “Simply Click This Button” button and watch the response.
In similar cases the solution was to uninstall IE9. Windows will automatically revert to the previous IE8 version and this might resolve your problems. Later on you can try to re-install IE9 again
See here how to uninstall/reinstall IE9.