Won't start
 

2001 C5 intermittently won't start. Usually I charge battery up and it works. Recently, after sitting used for a month, when I turned key lights etc come on but it just clicked. Now 5 days later, after recharging battery to 12.99 v, nothing happens when I turn the key. No lights, no nothing.
I am new to car repair and live and work now on Navajo reservation, 115 miles on from any reputable mechanic. 420 miles from mechanic who previously worked on car.
Ideas on how to proceed, at least to get it to good mechanic.
Thanks mucho