Thanks for quick reply!
1) How are you powering the Arduino?
I tried different methods: USB, 9V battery, 4x1.5V (AA) batteries (6.5V).
2) Measuring the resistance between the Arduino GND and the +5V pin is NOT a valid measurement or a debugging technique. The fact that two different Arduino boards measure the same would appear to confirm that they are both good.
3) You should be measuring the VOLTAGE not the current between the GND and the +5V pins. When the Arduino is powered (by the undisclosed method) do you see the expected 5V on the +5V pin?
I did try to measure the voltage from ground to 5V pin, it was always less than 5V, with any of the sources. Without the shield, the 5V pin was at 4V.
4) When you connect your shield board, does the voltage remain at 5V?
With the shield, the voltage was less, closer to 3V.
The tests I did were casual, and I'm getting these numbers from memory (I'm at home now and the stuff is on campus). I'll re-do the tests in a more organized fashion tomorrow and I'll try removing components like you said and I'll get back to you.
The schematic is a little awkward because I was rushing it to do the board to get the pcb manufactured in time. I'll reorganize it so its more readable and post it tomorrow.