The lock mechanism broke in my exterior door knob. I am probably going to have to buy a new one. Can i buy a new door knob and program it to use my existing key so I don't have to get new keys?
Doors – Is it possible to use the same key when replacing a door knob
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Related Solutions
In its currently disassembled state, there is nothing locking the mechanism. You are correct that the C shaped half-circle shaft is what pulls the latch back when turned.
If you cannot push the latch back with your finger, the anti-jimmy device has had a piece break in it.
I had this happen on a bathroom door latch about two weeks ago, probably made by the same manufacturer as the shape of the lock actuator rod and latch actuator are exactly the same.
If you look at it, the lock actuator rod (the center piece you were turning) has a taper section just where it passes through the latch pull which means that during assembly, you manually push the latch back and it passes straight through.
In order to get clearance so the lock actuator rod will pass through, I pried the folded piece that they pass through till I got clearance so the shafts would pull out. I then squeezed the folded piece back together and pushed the latch out. It didn't even require taking the door off the hinges.
Replace the whole door knob/latch assembly with new and you're back in action.
This style lockset is known as a mortise lockset.
Dis-assembly and cleaning won't hurt.
While you've got it apart, print the Baldwin diagram below, and note your dimensional differences. Some will be critical (holes for knob and deadbolt), others may be compensated for by strike plate adjustment or wooden block supports (under a shorter mortise body).
Backset (the distance from the door edge to the center of the knob) is a critical dimension that will determine what replacements are available. Modern backsets are usually 2 3/8", many older mortises are 2 1/8 and 2 (the new one below is 2.5)
This page lists some Baldwin mortises, they cover a range of backsets and door thicknesses. Googling "mortise locksets" will net you many choices.
Best Answer
Most brands of locks can be re-keyed, but it usually requires specialized techniques and sometimes tools. Many retailers will do it in-house free or for a small fee. Otherwise, any locksmith* should be able to help you out.
Be aware that keys have brand-specific cross-sectional shapes, so be sure to buy a new lockset of the same brand (or compatible with) the old one.
* I'll concede that locksmiths may have a slightly higher than average rate of crookery among them, but it goes without saying that any company performing service on or involving your home should be vetted properly. Any implies any reputable locksmith.