I also had the “always running, can’t jump” problem, and my computer is pretty much the kind you’d buy your grandma, so I figured it was up to the graphics card not being good enough. It’s also an all-in-one, so I can’t switch the card out. My roommate has a gaming computer, so he offered to let me try it on his setup and play while he’s at work, since I’ve been really, really eager to play it.
However, when we ran it on his computer, I didn’t have the running and jumping problems, but when I first began the game, the sky showed up as being almost solid dark and shady, and it ran really choppy. (Granted, the latter could be because the computer is 11 years old, so maybe that’s the computer causing the choppiness, but I’m not sure). I got as far as the first room/pool (the one you fall in) before it just started getting too choppy to continue, although the graphics problems seemed to dissipate at that point.