I second Heather G's recommendation for the Summer Infant handheld video monitor. We bought ours new in August of 06 and it's still working great. I can hear EVERYTHING with it, and I like being able to look in on my daughter whenever I want without waking her. It's been a Godsend when she's been sick. Also great for when they wake up, yell and go back to sleep-you can check to make sure they are okay and you don't wake them all the way up by going into their room!!
It meets all the criterion you list above. We live in an older house where the electricity interferes with cell phones and we don't get static on this. And we have been able to go outside across the yard with it and it works great.
One more thing, we bought a replacement adapter for the handset because we lost ours on a trip...they shipped it FOR FREE and we rec'd it in less than a week after we ordered it.
Finally, this is also a great pet training aid as we used it pre-baby to bust one of our dogs that kept peeing in the kitchen. This was money TOTALLY well spent.
Buy locally, check the return policy, and keep the receipt. Good luck!