One last question, did you measure the voltage right at the input pin to the regulator with the Yun connected?
One more last question What are you using for the tipping buckets?
Update!!!So today I tested my Yun with a new 5v regulator. Guess what? It works. So, even though the 'bad' one was measuring 5.01vdc Vout, when connected, the voltage dropped to 1.19vdc.
Sorry it took me so long to reply. I actually had a second regulator; same model and specs (5V, 1A). I considered the 3A one but it would be overkill for my project.
It will basically be a small weather system complete with two tipping bucket rain systems, GPS, TMP36 sensor and cellular modem.