Charging capacitor to power LED with a low current source
I am afraid you will never reach your goal if you mean 10,000uF electrolytic capacitor. The matter is that electrolytic caps have leakage. For example, Panasonic-made caps usually quote the leakage as "0.01CV", which means that your capacitor will have 0.01 * 6V * 10,000 = 600 uA of leakage. This will make it about as 10k resistor, so 15uA into it will charge the cap to maximum 150 mV. Which won't be enough to lit a LED. Maybe you can be lucky and your cap has smaller leakage, but not by much.

AMPLIFICATION/CORRECTION: I just tried a 10,000 uF cap,



It behaves a bit better than the estimations above. When charger to 1.2V, its self-discharge goes at the rate of 1 mV/s (as measured with a >10 MOhm DMM). With formula provided here by Spehro Pefhany, I = C*dV/dT, the leakage is about 10 uA. Still it means that a 15 uA 3.3V source will charge the cap only to about 1.3V, which isn't much for a LED.