This is a tricky one since we don't have a lot to go on.
Assuming I'm reading this all correctly, the problem is the black latch that's supposed to secure the ribbon cable inside the connector is broken and now missing.
There are about three main ways to deal with this. In order of preference and ease of repair, they are:
- Replace the black plastic latch
Obviously this is going to be the preferred solution, as it puts the board back to its original function with a minimal amount of work. So far the ongoing effort toward this has been focused on identifying the connector so a replacement can be sourced and from there hopefully it will be possible to remove the latch from the replacement and transfer it to the connector that's missing it on the board. - Make the connection work without the latch
This option has some possibilities that could work. The main thought here is that the purpose of that latch is to press the ribbon cable onto the electrical connectors inside the housing. This makes it possible to remove and insert the ribbon cable without having to force it in as is done with other kinds of connectors. Without the latch, the ribbon goes into the connector and the pins are all lined up, but there's nothing to press the cable and the pins together so you don't get a good electrical connection between them. - So in order to make up for the lack of a latch, what we have to do is increase the thickness of the flex cable such that it will make contact with the pins but still allow the cable to be inserted into the connector. I would think an easy way to do this would be to use a piece of tape. Place it on the side of the ribbon cable that doesn't have the exposed electrical contacts, right at the end of the cable. Carefully trim it to the exact same shape as the ribbon cable. Insert it into the connector. There should be some resistance, but not enough to keep it from going in. You'll have to be careful not to put too much pressure on the cable or you can end up bending and crimping it to where it will no longer work. The trick here is the thickness of the tape. I'd probably start with something thin like scotch tape. If that's not thick enough, you can try doubling up on it; use two layers. Or try a different kind of tape like black rubber electrical tape; that'll be quite a bit thicker. You may well have to experiment here to find the right one.
- Once you find a thickness where the projector works correctly, take some more tape and secure the ribbon cable to the socket to keep it from working its way out over time.
- Replace the entire connector
Of course, this is going to be solution of last resort, since it requires someone with pretty good soldering skills to be able to swap out a connector with 40 pins soldered directly to the circuit board. It also suffers from the same drawback as the first option; that of identifying a suitable replacement part. There's a little more flexibility here, as the part just has to fit the same footprint and take in the same ribbon cable, but the latch mechanism doesn't have to match yours; it could be completely different yet still work for your application if the entire connector is being replaced.
So as requested by @oldturkey03, I've started looking into sourcing a replacement connector. One question I have right now has to do with the orientation of the connectors. When you're plugging the ribbon cable into the connector, are the exposed electrical connectors on the bottom side of the cable, the side that's next to the circuit board, or are they on the top side of the cable? And just to confirm, those pins only appear on one side of the cable, not both right? There should be a plastic reinforcement/pull tab on the other side.
In the meantime, I'm looking and will let you know if I find anything interesting with regard to a replacement connector.
And one final question; when disengaging the latch, does it slide out flat, away from the connector, or does it lift up on a hinge and flip from a horizontal to a vertical position?
4/19/2023 Update
Here's the closest connector I can find.
Flexible Flat Cable Ffc Fpc 0.5mm Pitch 16pin
