Just had a user knock the base unit over here ( different make of pc ) but re seated the ram and it powered on again ( had similar issues to what you...
Not sure if it helps but don't youtube have a https site versus normal http ( see if that helps with uploading via https instead of normal http ) so...
If that is the case maybe it needs some ethanol or the likes to clean off the old thermal paste from the heatsink and cpu and re do the thermal paste...
Not sure if this helps but what about uploading them to youtube on an account that you can create or setup for the school and then embed the youtube...