Update: I have since pointed the webcam at the spot under the heat lamp, as it turns out most of the time there are birds there.I brought the monitor in for configuration only. I didn't want to leave in in there and get pooped on, plus it would be in the way. I have a hand-held trackball instead of a mouse, since the surfaces in the coop are... less than ideal for mouse use. The mouse is also a configuration-only item.
The trickiest part of this whole thing is getting an Internet connection in the coop. Actually, it wasn't that hard, once I figured out which equipment was best to use. The Dell is running Windows 2000 Pro, since that's the license sticker that came on the case when I picked it up at the surplus store. Windows 2000 doesn't natively support wireless networking. It will work, but it treats it like regular Ethernet, with a separate configuration app. Anyway my router is in WPA mode, and neither of the two wireless PCI cards I had supported it in Win2k (at least not with the drivers I had), so I went with my other option (besides running a cable to the coop--which would be doable, but require a purchase): a wireless networking bridge.
A few years back I picked up this pair of little black boxes on Woot, and they've come in pretty handy. They're supposed to have a range of 300 feet, and I have no reason do doubt it. Currently, I'm using them at about 75 feet, and they're doing just fine.
The stream is live, of course, so if the chicklings are being boring, or you're reading this later on, after they're grown and the stream is gone or of something else, you won't get to see the result on the live stream.
Therefore, I will post the following video, which I recorded as I was doing some final tweaks to the webcam setup, and saved it for posterity:
The voice you hear at the beginning is mine. I'm on my cell phone with my wife, who is in the house letting me know that the sound is working.