We were having an issue with large uploads this week -- PDFs and video. We have changed the "time-out" period that our server waits until quitting on you, which should resolve some of this.
Keep in mind that even if you are on a fast connection, your UPLOAD speed may not be as speedy as you think; often it's a fraction of the download speed. If you try to upload a 50Mb video file and you can only upload at 100Kb/s, it's going to take you a loooong time to upload that file -- up to 51 minutes.
If you don't succeed in the school environment, you might try it at home.
That said, here are some thoughts on how to make the file sizes smaller should this happen to you.
For PDFs, you should try to reduce file size. In Indesign, when you export to PDF, Web quality is one of the options and you should use it. Web PDFs are different from print PDFs -- images are smaller.
For video, every 1x1 pixel you go up in screen size, the amount of storage you require goes up exponentially. This means that smaller screen sizes usually translate into smaller files. Also, AVI files tend to be much larger than their cousins WMV and MOV; if it's an option to save in the other formats, try that. We're going to downsize them to our dimensions and convert them to Flash Video (FLV), anyway.