Innes, thanks for the video; it is invaluable! Sorry you’re having a little trouble getting your altura fired up, but congratulations on giving it a shot! It is a moderately ambitious project for a first-soldering experience. You seem to have been thorough in your troubleshooting. We are going to look at two things:
1) Are you getting 5V DC distributed around the board? Check the DC voltage to ground at a few places around the board, with the battery in and the power on. Consult the circuit diagram to spot the power pins on the MCU (marked VCC). Also the sensors are easy to measure. Unplug them from the board. One of the end pins should show 5V DC. What do you find?
2) there are three 14-pin ICs that look pretty similar: the multiplexer, shift register and hex buffer, located at U2, U3 and U4 respectively. Examine the nearly-invisible markings on these three components. Are they in fact three different components, with no duplicates? (It happened once.) Are they each in the correct location, in the correct orientation? Any error would account for the observed behavior.
Let us know what you discover.