You say that touch doesn't work "completely", so it works a bit? Is there one or more "band" on the screen where it doesn't register? If so, the circuit for that band is probably not connected. This issue could be a broken trace in the ribbon cable, a bad contact in the socket, a defect somewhere else on the display unit, or a defect on the mainboard. Maybe this is why the phone was sold to you for "cheap without the screen"? Try disconnecting, cleaning, and reconnecting the connector.
I'd also avoid buying anything from scammiexpress. You never know what you're going to get -- usually broken crap.
My suggestion is to order one from Amazon. If it has the same problem as the one you have now, then you know there's a problem with the mainboard and its time to cut your losses so return the amazon screen and resell the other parts with a warning about what's messed up. If it works correctly, then you know you got a bad screen from scammiexpress and can then decide how to proceed.