You've got to pull the inside upholstered panel off and take a peek inside to see what is not happening when you push the button. There is generally a pivot in there that is part of the latch mechanism, part of it gets activated by the button and part is activated by the interior handle. Something has probably rusted or broken away.

When you have the panel off, watch to see what the interior one is doing that the outside button is not doing.

Don