Cable and DSL service is optimized for DOWNLOAD bandwidth. As the sender, you'd need good UPLOAD bandwidth, and most places are restricted to 128 or 256 Kb/s. Plus, it's unlikely that a cable modem would work in a hospital. A cablemodem needs a fairly direct connection to the signal that comes in at the service entrance. The lines in the hospital rooms almost certainly are fed from a distribution amplifier that would prevent a cable modem from working.
Your best bet is to tape the event with a MiniDV camcorder and use its FireWire connection to pull the video onto your computer. WindowsXP comes with Windows Movie Maker which is surprisingly powerful and useful (much more than you'd think from free, bundled software), and is very easy to use. You could then email the movie, or put copies on CDs and send them out.
I know it isn't realtime, but I just don't see a cable connection as being likely. You'd have better luck getting them to install a DSL line for you, but you'd still have other problems, such as the upload restriction.
-Troy