Try cleaning cookies, cache and installing adobe flashplayer manually

Did you try turning on and off your computer ? Dont worry i'm an expert IT support ... guy, it works every time. :D

EDIT

THESE videos WON'T play on ANY PC connected to my network. Hidemyass changes nothing.

Some videos? Does this video work my little rainbow dash?
//edit: you don't need other videos!!

Have you tried disconnecting the power to your modem/router, waiting thirty seconds, and turning it back on?

I had a problem like that. I had to update Adobe Reader.

Clearing cache usually works for me when youtube videos are loading really slow.

If they are black, isn't that normally a playback issue?

Try changing quality level, or disabling hardware acceleration in Flash.

Its because they have ponies in them. Your internet has had enough. You better stop trying to watch them before it turns to suicide.