This sounds frustrating, after all that work.
Pins 3, 8 on the LTS-2301AP LED display are shorted together internally (for common cathode) but I see traces and a connector to it, so maybe LED pinout is wrong?
I would double-check the new display board pinout with a multimeter on diode-test, on the bench.
Maybe check if the LED pins are shorting to the main pcb, it looks very tight.
b seg. P1-1
g seg. P1-2
e seg. P1-3
N/C P1-4
CC digit 1 left P1-5
CC digit 2 P1-6
CC digit 3 P1-7
CC digit 4 P1-8
CC digit 5 right P1-9
N/C P1-10
dp P1-11
d seg. P1-12
c seg. P1-13
a seg. P1-14
f seg. P1-15