STOP!
Don't mess with the board-to-board connectors (the ribbon cables Voltor describes). Voltor, please do not advise people to open their LPs and *&%# around inside them. That's my job!

Plus it's a good way to void your warranty...
In all seriousness, the reason it's my job is because I have a pretty good idea how these critters work, and what actions may be helpful or not given a particular problem. In this case, those board-to-board connectors are not associated with the stated problem, and so nothing good would come of messing with them.
It is possible, though not probable, that the cable from the keyboard to the digital board is slightly loose and could cause this problem.
First thing I would test to diagnose this problem further is what happens when you hit the octave up/down buttons on the keyboard. This shifts which octave the keys are playing. If the problem is with the physical keys, then you can transpose the keyboard octaves up and down and the same physical keys will continue not to play, even though if they were playing they'd be playing notes an octave up or down...
If it's four keys all in a row that are not working, then the likeliest cause is a broken diode or similar hardware fault on the keybed assembly itself (keys are scanned in groups of four). If the four keys aren't all in a row, then something stranger is happening.
If you got this synth from an official Moog dealer, my advice would be for you to contact the dealer and see if they have a unit in stock they could swap with yours... then we can repair the fault without inconveniencing you further. If they don't have a unit to exchange, then contact me directly and we can decide on the next best course of action. I can repair the unit here or I can send you a replacement keybed to install yourself, if we determine that this is definitely the source of the problem.
I'm very sorry for the trouble!
Kind regards,
Amos Gaynes