You say the paper looks to be twisting (skewing?) as it is being pulled from the tray. That still sounds like a problem of the paper not being flat (broken hinge of the lift tray) against the roller. If the paper tray is level, then perhaps the roller is not level.
Check to see if the roller shaft or roller/feed assembly isn't bent. You could always try putting a thin coating of toner on the roller to see it's 'footprint' on the paper.
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