Looking at the other post you got some reasonably good advice but your problem is still not solved.

Can you measure the interior dimension of the frame and exterior dimension of the wood for me? The frame should be 1/4" larger than the door. I guess it is possible the multiple layers of paint over the years have caused this to be closer to 1/8" or 3/16", it looks a little tight in the picture. It may need to be cut down a a smidge just to make everything work again.

If it is the right dimensions then its really tough to give good advice without getting my hands on things. Reasonably as long as you have a 1/8" reveal all around and the correct hinges you should be able to adjust them so they function appropriately. Did you mount the new hinges following the instructions of the new hinges or in the same mounting position as the old? they may not be directly equivilant in all respects.