I took it apart, there was nothing in the way. The hinge was broken- that's why I had to replace it. So I just installed the new hinge as is. It turned out that the hinge did rotate when it was attached to the screen. It's a very tight hinge, as I can now see. It has to be tight so the screen isn't floppy loose.
I put it back together successfully, which means I didn't break anything in the process. Along with the new keyboard that I installed at the same time, my old laptop has a new lease on life.
Thanks for your reply.