I think you could design something that could communicate that weighed less than a pound.
You have line-of-sight, and at the earth end you can build (or just rent) a huge antennea and use huge amounts of energy to send the signal. Think about how they talked to pioneer and so on -- those are much further away, and we detect billionth of watt signals, and blast huge signals back out.
I think the optical communication is interesting, because earth bound telescopes might be able to pick up several super LEDs. The bandwidth doesn't have to be huge -- you can morse code that light very slowly, 2 seconds on is a 1 and 1 second on is a 0, or even slower. It can take a week to transmit, and only transmit when the moon is in shadow, to be sure to give good contrast.
If commands must be sent to it, radio will be the best I suspect. So much work in the history of radio has gone into learning how to make big, power transmitters and tiny, cheap receivers. You will have to have a key embedded in your rover so that some joker doesn't send it the wrong commands for you.
I thought about this google challange thing, and I figured a tiny rover with motors from cell phone vibrators, an atmel chip wrapped in foil, a capacitor storage and tiny photocell, would be best. It would be less than the size of a pack of cigarettes, you would aim for a smooth part of the moon to the extent that you could aim, and hope that it move in spurts over the course of a few months. You might be able to drag a thin hair-like copper wire in order to get a longer antennea for receiving.
It might cost 10k per pound to launch to low earth orbit, but I don't think you can buy 1 pound for 10k dollars. In anycase, if you were in low earth orbit, how would you get to the moon ? You could try to do the solar sail thing, maybe agmented by a tiny occasionally firing ion thruster powered by photovoltaics, but in low earth orbit the sails will have some drag that might pull you in before you ever get started.
So I still think you need a million or more dollars, and the orbit to moon part is not solved.
If a company were formed to do this, and shares were sold to raise money; if the share holders could vote on officers and major decisions the way the Debian community does, or via a system such as www.DeliberativeAssembly.com; I might invest never expecting to see my money back, but hoping the effort would lead to something interesting.
By "invest", I mean one stock should be between $100 and $1000 dollars, and I would by one.