The command prompt is working, but the ping command is "missing".
Try this:
At the prompt change your directory to "%systemroot%\system32\", once there try pinging again. If it works, I would guess that some of your system paths have been changed, if it doesn't work, at that command prompt, which should now look like C:\Windows\system32\>, type in "dir *.exe" this will list all things in that folder with an exe extension, look through the list and check for ping.exe.
Let us know what you find and if any of this has helped.