Before we go ahead and assume it's actually gone;
Snipping Tool, like most built in Windows programs, is located at C:\Windows\system32 Not Program Files. The full path is:
C:\Windows\system32\SnippingTool.exe
Try pressing Windows+R (the key with the Windows symbol on it, usually 2nd one in on the left at the bottom of your keyboard) and pasting the above in, see if it loads.
How to use the Snipping Tool in Vista and Windows 7