You can leave out a screw or two if you want, no problem there! You can run with no screws, or as many as you want!
Sounds like you might have had a short or something before, or the motherboard mounting peg (Stand-off) that the screws go into isn't screwed in all the way, causing the board to flex or short. You can remove that peg (Stand-off) if you want, and or leave out the screw, or try to screw it back down into the tray fully, then you might be able to use the screw properly.
Sorry, I'm not sure what you were trying to explain about the screw but I think that's kind of what you meant right?
Anyway, good to hear it's working properly for you now!!