I've had that turn out to be a broken latch assembly. In this case it could also be a bad link that is preventing it from unlocking, or a bent mechanism in the handle. More common on rears, when the latch gets rusty, the pushbutton, instead of pushing the lever in the handle, bends it, and it eventually won't open at all. You can unbend it if you get it before it breaks.
In any case, if you have to remove a door handle, and it's rusty, go slowly and use lots of lube. The door handles have nuts on studs that are easy to shear.
If you do shear one, you can grind the stud flush and drill into the body of the handle, but you must use a very sharp drill and do it slowly or in stages so that it does not heat up, or it will melt the insert in the plastic handle. Use the tap drill size for 1/4 inch NC, and tap the hole, and it will work fine with a short bolt.