Radek

The problem may be in connecting the Uart inputs to other pins at Fysetc and BTT. https://theres-probably-a-better-way-to-do-it.readthedocs.io/en/latest/pages/electronics/skr_1.3_and_fysetc2209v3.html  

Versions FISTEC 3.1 and 4.0 have a different connection Apparently a good company :-/   https://wiki.fysetc.com/Silent2209/

Open the pdf file from this repository in acrobat reader. and you have the option to search for individual pieces that are highlighted on the board For example, U3 is...

the schematic is here too... 

If you checked fuse F2, there will be a problem with the 5V regulator.  

Can you also check fuse F1?  Put the jumper in position VDD Measure the voltage at both ends of fuse F1. It should be 5V at both ends.

@landif writes that he has revision B

Revision A has used an inappropriate Mosfet, which will cause TMC drivers to burn out and other problems. Version B should already have the correct Mosfet type. This board has...

Good. The fuse looks fine has 0 Ohm. Turn on the power. Remove the VDD jumper. Measure the voltage at the VDD pin. 

So you have a problem with the 5V source. There are 3 solutions: 1. Complain the board to the seller. 2. try to fix the 5V power supply integrated on...