Thanks for checking. I really expected the problem columns to have moved. IC's U5 to U8 control each column of LEDs. U5 controls columns 11 to 28 and U7 controls columns 51 to 68 which happen to be the columns that aren't working. So this points to a problems with those two IC's. However if that was the case then swapping them with the working IC's should have moved the problem to the other columns. Also the data pins on these ICs are daisy-chained (cascaded) so if U7 was dead U8 wouldn't work and if U5 was dead none of them would work. I would next point at the actual columns of LEDs but you have already checked them.Yes, swapped ICs around, same rows failed
My next thought is the components around U5 and U7. The only components I can see that could cause this problem are resistors R8 and R10. Looking at the original image you posted I can see that you have fitted the correct values (1K) but can you check the soldering for these two components. I can see some flux around R8, was there issue with it?
Failing this I'm not sure what else it could be. If you still have no luck I'll take a look at the PCB layout to see if its possible for a problem with a track or a short somewhere to cause this issue.