Open Source Video Editor
Well this looks interesting, a free open source non-linier video editing package. Now if only it ran under Windows :) (kickstarter for just that: Link)
There is a live CD though and it seems to support a stack of codecs.
A director is pledging to use it to make their next movie Alex Cox directs BILL THE GALACTIC HERO by Alex Cox » BILL SUPPORTS OPENSHOT — Kickstarter
Yes just editing to include that but for some reason EG is taking upwards of 60 seconds to process my posts at the moment.
Looks like it is well on the way to its extended goals and it should be a great alternative for schools.