If you use a bigger flathead screwdriver, you should get more pressure? Or find a flathead screwdriver with a bigget bit so that it fills up the track in the screw?
As PDM says, reconnect the connectors, and also disconnect the battery to do e power cycle. Also check for dust and dirt in the connectors on the motherboard :-)
How do you guys usually do it, when you are doing an lcd replacement, always use the scotch tape and black marker trick, or do you first replace the screen and then test if the proximity sensor works? And then if it not works, you have to do a re-assembly again?