First test, and firsts problems

Hi,

I would try to help you the best I can:

I think something goes wrong because the pedal led does not light on

Are you sure that the led is soldered in the right position? It is a very common mistake the solder it the other way around, Have a look at this pic, the "bigger" metal part inside the LED is the negative pin, make sure it goes to the negative pin. It is pretty small but you can see it:

You can also open the arduino due example codes and just use the blink code to blink the led (pin 13 )

BoosterPedal. It seems to work, but the increase is very, very tenuous,

Make sure that the VR1 potentiometer is at a good level, this potentiometer controls the amplification of the guitar signal going into the Arduino ADC, try playing and moving it until you feel it sounds good.

the background noise is quite large

The noise is probably coming from the poser supply, have a look at this:
www.electrosmash.com/forum/hardware-peda...-arduino-due?lang=en

After trying distortion effect this do not work. It's the same sound but with noise but not distortion

Distortion effect could be tricky, some guitars are tricky, try playing with the variables that set the threshold levels in the code, the sweet spot for a good effect can be quite reduced, I usually need some time adjusting this values for one of my guitars.

Enjoy the debugging!