It is a sad fact that digital pianos aren't made to last. The action inevitably decays as the metal parts wear away the plastic ones (often there is a flat metal spring that pushes against the plastic key).
There is a chance you'll get casio to fix it under warranty,, but I wouldn't hold my breath wating. Look for an "authorized service center", which you can probably find on casio's website. Even if they do agree to fix it under warranty, it's likely to take a long time-- or even if you pay for the work.
I've never taken apart a casio, but my Yamahas have turned out to be relatively easy to open up, once you figure out the trick. And there are definitely tricks to figure out. Maybe you can find a service manual?
Replacing the keys seems to do the trick for me (or, more often, switching the worn keys in the middle for the less-used ones on the top or bottom).
I would definitely encourage you to busk! It's kind of a crazy idea, but often that's what it takes. Pursuing a performance career is a crazy idea to begin with!

I bet you could rig a car battery, though I wouldn't know how. Generators are pretty loud, probably louder than your keyboard's internal speakers (if that's what you are planning). Probably you'd want some kind of keyboard amp or powered monitors, which of course means more power consumption. How about trying a long extension chord, and asking some business if you can borrow an outlet for a little while? There's got to be music lovers around somewhere:)