You may have a corrupt Control Panel file. The way you can test this is to remove the control panel files from your system and put them back one at a time until you find the one that is causing Control Panel not to open. First make a new folder on your desktop. Then go into My Computer and browse to your Windows\System32 folder. Right click that folder and choose Search. Under the All or part of the file name section type in *.cpl then click on Search. It will find all files in the System32 folder that end with cpl. Now highlight them all and choose cut (not copy). Go to your new folder on your desktop and paste them into it.
See if Control Panel opens. If it does it will be empty but that's Ok. Now copy back each cpl file one at a time from your desktop folder back into the System32 folder. Each time you copy one, see if Control Panel opens. Keep doing this until you find the cpl file that causes Control Panel not to open. Then once you find it you will have to get a replacement copy of that file. You can get it from another computer running Windows XP and copy it over to your System32 folder. Since you said you were having problems with Add/Remove Programs that may be the faulty file right there. The file that controls that is called appwiz.cpl. You may want to check that one first.