
The problem is definetly the display since it is only 1 segment missing on one digit.If you can zone in on that wire bond, silver conductive epoxy may be able to repair it.Otherwise you will have to carefully remove the display and try another one.
Then again you could try to connect 13 wires soldered to a display you want to test to the 13 pads on the board.If you leave the old display in while doing this both displays should light.
Don't forget to check the 2 additional segments on far left that gives you the l for TU esday and TH ursday.Also the one extra segment on second digit from left that gives the slant in R for FR iday.