My guess is that you will find that the pump is frozen with a piece of oil coke and/or a piece of valve seal having gotten stuck between the rotor and the body. Once you take the plate off of the bottom of the pump and drop the rotor and remove the junk you should be able to use it again. If the sides of your oil pan are coked up it is proof that your oil has a lot of wax in it and is not cleaning as it should. That is why I switched to Mobil 1. Since I did, I haven't had this problem and everything is very clean. Prior to that it happened three times. I was using Pennzoil which has slick advertising but also has a lot of wax. Besides causing the gear to break on the distributor, it can case the roll pin that holds the gear to snap, it can twist and then snap the oil pump drive shaft and it can also knock teeth off of the cam gear. I've had all of that happen over the years. In my humble opinion, that design of the cam gear driving everything else is the one downfall of the small block Ford, while it is a good design theory. While you have it apart, a new pump might be a good idea because they are inexpensive and if you haven't changed it in a while, you'll get better oil pressure. I use Melling standard pressure, high volume pumps. You might also try to get a high tensile strength oil pump drive shaft. I think Ford Motorsports sells them and the dealer might even have one. I rev mine pretty high for a pushrod engine and that is when the failures have occurred.
Submerge the oil pump in a bucket of oil and rotate the shaft with a speed-handle and socket. You should see it pump oil out of the top. However, this will not tell you the volume or pressure but it will tell you if it's binding.
Another idea; before you drop thepan, pull the distributor and use a socket on an extention to see if you can rotate the oil pump drive shaft. If you can, it's not the pump. If you can't, it is. Might save you some time.