How to light an LED with very low voltage and low current?
This is going to be very difficult at best.  Transistor circuits don't work with just 100 mV power supply voltage.  If you really need to run something from this low voltage, the circuit will need some initial external power to get going.  This could charge up a cap to a few volts, which could then run a boost converter which would boost the 100 mV up to the few volts to keep itself going.  This is of course assuming there is enough power available to not only run the circuit at the higher voltage after conversion losses, but to have enough left over to light up a LED to a noticable level.

Let's say you get the best efficiency LED you can find and that it is bright enough a 500 &micro;A and drops 2 V in the process.  That's 1 mW.  Without conversion losses and power needed by the circuit, that would mean the 100 mV supply would need to source 10 mA.  If your 100 mV supply can source a few 10s of mA, maybe you have a chance, but you'd still need some initial external energy to get the bootstrap process going.