may I ask:
can you start up both distro's to graphical desktop???
I think that Safe mode or something like that might help if you don't get to the desktop environment in the live-cd (Mandriva)
when a distro is installed and show a black screen, try
and log in as root
(maybe you have to use safe mode or another boot option)
=> then try commands like xorgconfig
=> one of them is for graphical environment) or video
: configure with low settings (experiment!)
(these are only suggestions, maybe there is something else wrong)
If this doesn't work after some tries, post it here!