You can hopefully take it all apart with a screwdriver. You might be able to clean any gunk/oxidation from electrical contacts.
The insides of the ones I've seen(Yamaha, M-Audio) all use a silicone membrane tap type switch like in a PC keyboard. For velocity they use two, one is physically lower or hit later, so it's based on the timing of how quick the second membrane button is hit after the first. It's interesting how they multiplex 64 Keys down to about 12 wires with a bunch of diodes and resistors. Thankfully those probably don't go bad often.
One trick is to move key components too a less used spot. So, broken keys, move it from middle C to farthest away it will fit and less likely used. You might be able to swap these rubber pads to a lesser used position if that is the problem. Sometimes they lose shape, or contact part might get worn.
Or heck, maybe the best solution is just to smash or burn it on stage and buy a new one

Sorry, it's like environment day, so I had to throw that in. Browse the second hand market, I find used Yamaha and M-Audio keyboards for a song and a dance.(cheap). I have had some experience with a buddy's higher end Yamaha Motif, and I had a nice full size Yamaha weighted unit once. The motif has some neat layered sounds, but some the keys broke easily and it was really way too heavy(the whole keyboard, like 40lbs). The weighted Yamaha unit was nice enough, I wouldn't mind having one of those again(I got rid of this one, moving, needed space/money..) But, I really could never groove on the whole synth sound having had a real piano. Now I'm quite happy geeking out with my odd cheap plastic keyed synths and lucky to have a real piano(even if it is a beater) to satisfy my string and real sound fetish.
I've had a Axiom 25 for not too long. I was kinda excited to try the aftertouch, but then when I got it and tried it, it was like, this is stupid, it doesn't really do much does it

I believe it is advertised as 'semi-weighted', it does feel a little nicer than the cheaper units. I haven't taken that apart yet

the buttons and knobs are higher quality than the keystations. I'm guessing it's got the same or similar guts(rubber pads, etc). The keys on the weighted Yamaha I thought were nice, and the built in synth is nice enough. The Axiom has 8 drum pads that I'm fairly impressed with, although I haven't played with it much. It's made of a thicker rubber pad that seems to react OK. I've got this old DK-10 KAT drum pad, it's got to be 20 years old at least. But it uses a different sensor type than say the rubber contact switches for keys, uses I believe some resistive rubber element or something more analog. I'm guessing the Axiom has that for it's drum pads. I'm guessing all the keyboards use the 2 rubber contact type of switch, the higher end Motif I believe did. I'd be interested to know if any other Brands used different technologies. I do not have any experience with some of the other higher end key units(Korg, ...). I once had a old Fender Rhodes, but like an idiot I gave that away
My wife thinks I have too many keyboards

She's probably right

Are you in the US? Maybe I could sell you one for cheap

Good luck with your fixes or bargain hunting!
Oh, and PS, I picked up a used keystation lately that the keys don't work at all, the pitch bend and other wheel work, I've had it apart two times and now I've given up on it, maybe you could use it or some of it's parts...