Why is my iPhone x don't turn on

Unplugging the battery before disconnecting any other connector is always a good idea, but it's most important when replacing LCD screens, as even a slight misalignment can short out the backlight signals and blow a fuse on the motherboard or fry the backlight circuits on the display. With the newer OLED screens like yours has, it's not nearly as common for that to be fatal to other components since it doesn't have a backlight.

So it may not necessarily be an issue with the new screen; you could always test that by plugging in your original screen and seeing if it lights up. If it does, you'll need to get yet another screen, and if not your new screen is probably okay and something else is the problem.

I would probably start with the cable you say you cut. I'm guessing you're referring to the proximity sensor, which is part of the earpiece speaker/front sensor assembly. That assembly could be the reason your screen isn't displaying anything, as it contains both the ambient light sensor and the proximity sensor, either of which could keep the screen from coming on.

If indeed that's what happened, your next step really should be to replace that assembly. Be aware that now that the old one is shot, you won't get Face ID working again unless you pay Apple to replace your screen. Their screens come with the front sensor assembly already installed, so you'll be getting a new one and they'll be able to get Face ID working again as well.

Should you elect to replace it yourself and are willing to live without Face ID, at that point the screen should come on; if it still doesn't try testing your old screen with the new sensor assembly and see if that works; that way you'll know if you've somehow fried the replacement screen. It's always possible you just got a bad one.