Hmm... your pic is too small to see so I tried to find a bigger one, the best I found was this which is very similar but not identical as the thin LED ribbon looks to be slightly more left on yours.
Looking at the ribbon on the 'wrong' board (which may have been designed by the same person) there are 6 wires separated on the spacebar side leaving 22 other pins. There's a similar looking spit in your pic but I can't count them - is it the same?
I also notice that the two pins on the spacebar side are separated at the connector end and again it could be the same on yours. If so they could be for the power button in the top corner so it's actually a power button rather than a keyboard key? If not the extra 2 pins could be for the Caps LED.
Not sure what you're using to find connections but high ohm doesn't sound good - either the pins are connected (nearly 0 Ohm) or they are not (infinite Ohm) The easiest way to check is using continuity mode where a multimeter will beep if there's a connection, so you don't have to look at the screen.
Another thing we don't know is whether there are diodes on this board. If you know which two pins any switch is connected to test it one way then swap the probes - if it only shows connected one way you have diodes. This will make it harder to find the pins but makes it more likely the matrix is easy to understand as the designer doesn't have to worry about ghosting.
Hope some of that made sense, if not please ask