Check the fuse's, I blew one years ago and it would only run when key was on start, but died as soon as you stopped cranking.
If they are all good, grab a can of aerostart and give it a spray and she if she runs.
http://www.skylinesaustralia.com/forums/topic/406270-tas-wrecking-s1-turbo-r33/
should be able to get most of the bits to fix it off that /\
Only need basic tools to replace the ignition, or call out a locksmith to do it.