PowerPC desktop Mac black screen fault?
PowerPC based Macs are old, too old to run Yosemite by a good number of years so I'm going to guess that you have a MacPro and an Apple Cinema Display in which case:

http://support.apple.com/en-us/ht2811

Should help.

Edit:
I should expand on my rather terse answer. I think that the timing of you upgrading to Yosemite is a bit of a red herring. The problem according to the KB article seems to be to do with the power supply. It may have been damaged in some way (or maybe just 'got old'). Check everything is plugged in snugly and that nothing is shorting (no hissy-poppy-crackeling sounds). Also check for excessive heat coming from the power adapter. It shouldn't be too hot to hold, if it is it implies some form of damage.

~W