I want to broadcast videos - where for free

I doubt that you would find a free site that would allow you to do that. Broadcasting videos uses a lot of bandwidth and free sites usually permit you a limited amount per month so you would probably find your site locked after about 1 day of activity.

I'd also be very wary of free sites for another reason, their terms of service agreement. If you post a video on Youtube for example, Google acquires the rights to use your video in any way they wish without compensation. Verify the TOS before using any free web site option. You'd be better off setting up your own site which really isn't very expensive these days.

You can try this: https://mycast.orb.com/orb/html/login.html It's quite easy to use and the videos resides on your computer. The only problem is with the limited upstream speed of most internet home connection and whatever transfer cap you might have. But it's 100% free and requires no hardware purchase.

There's also some hardware you can get (external storage like this http://www.dlink.ca/products/?pid=509 for example) that have a built-in streaming server. Again, the drawback is using your internet connection with the speed/transfer limit.