When nothing lights

Start with the symptom

Almost every fault on this board is one of five things, and each has one check that settles it. Work from the symptom rather than from the wiring, because rewiring a chain that is already right is how a working display becomes a broken one.

The two measurements worth taking

Twelve volts, against your board's ground. Black probe on a GND pin of the microcontroller, red probe on the module's 12V pin. Twelve volts there means both the supply and the shared ground are good. Reading it against the supply's own negative lead instead proves only that the adapter works, which was never in doubt.

Continuity across the join. With everything switched off, a continuity test from the first module's DATAOUT pin to the second module's DATAIN pin. That single link is the one connection in a chain that is not duplicated anywhere, so it is the one whose failure has a symptom of its own: the near module counts and the far one stays dark.

The faults that are not electrical

Two of the five are in the sketch, and they have shapes you can recognise.

A flicker while the number changes is the latch being pulsed between bytes rather than once at the end. Move the two digitalWrite(LAT, …) calls outside the shiftOut loop.

Digits in the wrong order is the array being filled the wrong way round. buf[0] goes out first and therefore travels furthest, so it is the leftmost digit.

Neither of those is worth a meter, and neither is fixed by moving a wire.

When it is genuinely the module

Rare, and it has a specific look: one segment that never lights whatever you send, on one module, while everything else behaves. Send 0xFF — all seven bars and the point — and any bar still dark is that segment's own line.

Swap the module with another from the box before concluding anything. If the fault moves with the board it is the board; if it stays in the same position on the bench, it is the wiring or the joint feeding it.