Because of the previous post, I decided to test a bit more. To see if I could physically move the board to reduce interference. So I connected the Arduino with the attached RFM12B radio module. The one using the Sparkfun MIDI breakout board. As I was clearing the desk, I placed the Arduino on a side table, still attached to the computer via a USB cable.
Suddenly, most of the interference disappeared! The Arduino was receiving the messages from the EM-1 every ~2.5 seconds. I then tried moving the board around. The amount of interference would go up as I got closer to the computer of the computer screen.
I decided to try the same thing with a Jeenode. I could not repeat the situation. Interference was uncontrollable with it.
I tried every different board I had: Arduino Duemilanove, Arduino Uno, LadyAda DC Boarduino. At first, I thought that the FTDI was causing the problem, but the same chip is found on the Arduino. I tried different FTDI cables and boards. I even tried battery power. There seems to be no way to get the Jeenodes to behave! I will have to find out what the differences are between the Jeenode and the other boards.