To make a long story short the pump disintegrated and then seized up.
The part that failed is called the wobble plate. Here's an animation of a wobble plate pump. The rotating disk is also called a swashplate. It converts the rotation of the engine into a reciprocating force to drive the pump pistons. This video shows how a wobble plate (swashplate) is made -
I looked at parts to repair the pump and they were pretty expensive. The wobble plate and needle bearings had come apart and pieces were in the pump oil...so I wasn't totally sure how long it would last even if I did replace the plate.
I ordered this replacement pump from Amazon -
Briggs and Stratton 207365GS Pump Kit for Pressure Washers
One tip would have made taking off the old pump a lot easier - you may need a bearing/gear puller. Autozone will let you borrow one if you leave a deposit which is refunded when you bring it back.
The new pump slides on the crankshaft once you get it lined up just right. There's a woodruff key in a keyway on the crankshaft that has to line up with the keyway on the pump. The pump is mounted to the pressure washer frame with 3 bolts.
The time consuming part for me was figuring out how the old pump housing was mounted to the engine. I removed the 3 bolts but it wouldn't budge. I disassembled as much of the pump as possible to try and see how it was attached and finally figured out it was a typical keyway shaft affair. After 10 years or so the crankshaft and pump were pretty well mated together due to corrosion. I tried PB Blaster penetrating oil but I didn't want to hammer on it and damage the engine bearings. Using the bearing/gear puller it took about 5 minutes.
That new pump cost me less than 1/2 the price of a new pressure washer so I'm pretty happy. It has more pressure than the old one ever did.
A few tips for keeping a pressure washer operating - don't let them run without water ever (the pump gets hot fast without water), if you aren't spraying turn it off - they have an unloader valve that should open when it reaches a certain temperature and allow water to flow out of the pump but it's still getting hot and that valve may not work, and use a hose that doesn't leak and has adequate water supply - if you let the pump cavitate (suck air) it will beat itself apart.