Chosen Solution

I am repairing a tablet for my dad, and I have on two occasions tried to “unlatch” the ribbon connectors, but accidentally broke off a piece of plastic because the side I was pulling up on was the wrong side, opposite the side with the latch that I am supposed to pull up to free the ribbon cable (in the attached picture the latch is the white side of the connector). Sorry for the confusing terminology. The side that I broke the piece of plastic off of has pins underneath the plastic, should I be fine as long as the pins are still there?Google photos

A X there is a good chance that it might still work. The connector is not just holding the ribbon cable in place but it also provides pressure on the contacts to the cables. So, use some downward pressure and apply a piece of electrical tape over that area to exert some pressure.