Generac Pressure Washer - Stopped after replacing pump

I inherited a Generac G24V Pressure Washer that had sat idle for at least 5 years. I cleaned the carburetor and was able to get the engine running, but had very inconsistent pump performance. I adjusted the unloader valve, but couldn't consistently get it to run.
 
The hose and wand were rusted so I ordered a new pump, hose, and wand and replaced them all this afternoon. I ran water through the pump, hose, and wand with the engine off, then started the engine and everything worked fine. Pump had pressure and I was happy. 
 
After a few minutes, the engine started bogging down (particularly if I set the wand down for a few seconds to get the next item I was cleaning). When I pressed the trigger, the engine went back to normal. I went to change a nozzle, and the engine bogged down again, and this time, it died.
 
Now, I can't get it restarted. Not only that, but the pull cord is much harder to pull -- it's almost like I'm pulling through molasses.
 
I've replaced almost everything but the engine.  What should I check next?