I know the $PATH has already been mentioned and you said the \windows\system32 directory was in there, but you might want to try running the commands with the full path anyway just to test. Something like:
\windows\system32\ping 192.168.1.1
The last time I saw something like this (on a 2000 box, so \winnt instead of \windows) that got it to work. No idea what causes it though.

-Magnus