Here is the trick to get to Add/Remove Programs window without Control Panel:
(It works in pretty much in any Windows from Windows 95 to Windows 8)
Press Win+R, in a Run window paste this
As for a problem, my guess would be that you have got some custom Control panel file (*.cpl) installed, which is messing up your Control panel.
Therefore, I would search Windows\system32 and/or Windows\SysWOW64 folder for *.cpl files and examine everyone individually to find out an odd ball. Likely, there is one, which is causing the problem (it happened with me once, when I tried to install some drivers in Compatibility mode, it installed some cpl file, which was not working).