I seem to recall there are only the two screws, but a quick feel around inside the door should confirm this. There should be one at the "tail" end and one near the button end.
Usually, there are these silly little plastic clips that hold everything together as far as those linkages go - have a look at the inside latch and lock button for an example. Often, when some part of the door linkage quits working, it is due to the fracture of one or more of these silly damn clips. They can be had in original Nylon or sometimes in spring steel with a brief perusal of the "HELP!" section at your local parts house. The breakage of a rod is rare, and it seems that if the problem is in the handle, it is the handle itself that breaks (they are typically sintered - powdered metal in a mould, then pressed and heated. Cheap to make in bulk...)
As long as the handle itself is find, I'd check for those little clips and see how many need replacing. Try to get the spring steel ones if you can - they work just as well but take rather longer to break...
5-90