Getting some odd (to me) results...
If we number the displays 1 to 4, left to right, with 1 being the faulty one
The only continuity is between pin 10 on 2 to pin 10 on 4

Hello,

Can you check continuity between pin 10 of the faulty display and pin 10 of the others?

Bertus

 

Put the positive lead on one of the anode pins and, with the meter on diode check, put the negative lead on the other pins one at a time until you've verified that all of the diodes are good. You should be able to see each segment turn on. As you're doing that, you can draw the pinout for the displays for future reference.

The meter in diode mode is NOT likely to work because there are two LEDs in series. With Vf 6-7 V, the diode test will do SQUAT. with a 5V supply and a diode drop on the transistor, it just might be out of tolerence.

The best you can likely do is to pick a high range in ohms like 10K and with power off, follow the "g" trace from U1 to the IC. You should get ~330 ohms. to the pad of the display. Use the IC pin on the top as well as the bottom. If that's OK, you could look for some activity on that segment with your voltmeter in AC or DC when that segment is supposed to be lit. Check a good segment first.

Differentiating between the display and the processor is reserved for a later time. I'm guessing, bad display.
With the DVM in diode mode you'll get overflow in both directions (leads revered), if it's bad or good. If it happens to read less than 5V in one direction, then the display is faulty. But a 6V max Vf on a 5V supply is bad design.

Other tests are possible.

 

Hello,

The third digit is turned around, so pin 10 should be on the other side of the PCB.

Bertus

 

The meter in diode mode is NOT likely to work because there are two LEDs in series. With Vf 6-7 V, the diode test will do SQUAT. with a 5V supply and a diode drop on the transistor, it just might be out of tolerence.

Where do you come up with two diodes in series?

 

Where do you come up with two diodes in series?

Take a look at the datasheet.

 

Hello,
The third digit is turned around, so pin 10 should be on the other side of the PCB.
Bertus

UPDATE:
I now have continuity between digits 2,3 and 4 on pin 10.(having checked the correct (upside down) pin on 3)
(Thank you again bertus)

So, only digit 1 (on the left, the faulty one) has no continuity through Pin 10

 

Take a look at the datasheet.

Here is a data sheet for a similar part.

The datasheet is for common cathode and it hasn't been established that the OP's part has two LEDs per segment...

 

Where do you come up with two diodes in series?

https://forum.allaboutcircuits.com/...ject-build-a-clock.133519/page-2#post-1110944

 

The datasheet is for common cathode and it hasn't been established that the OP's part has two LEDs per segment...

That isn't the datasheet I was referring to! I was referring to the datasheet for the part the TS is using. See KeepItSimpleStupid's post.

So happens I am familiar with that part and its family. I have used it before in a couple of projects.

Friendly advice about to be offered. Scroll past if you desire.

Don't jump to conclusions! Think outside the box when something doesn't seem right and look for an explanation. IMHO...

 

Hello,

I assume the PCB is double sided.
Could it be that you forgot to solder a bridge between the top and botton layer?

Bertus

 

UPDATE:
I now have continuity between digits 2,3 and 4 on pin 10.(having checked the correct (upside down) pin on 3)
(Thank you again bertus)

So, only digit 1 (on the left, the faulty one) has no continuity through Pin 10

To test whether the problem is a connection, such as hidden below the display or the display, then try soldering a wire between Display 1 pin 10 and Display 2 Pin 10.

 

Yeeeeeeeessssssss!!!!!!

 

First: A temporary link to see if it made a difference. Middle segment lights - brilliant.

Then a more permanent fix (bertus, the fuzzy photo - just for you )

Job done. Solved. Completed

Thank you all for your help, it's greatly appreciated.
I am inordinately happy.

 

Almost done.

Take the seal off the buzzer.