Troy Bilt Power washer with Briggs and Stratton engine, Pull start, no primer only choke.
New Spark Plug
Won't Start any suggestions

Did your check for a spark, disconnect the plug wire and hold it close to the plug while you pull the cord and check for a spark. Hint hold it with insulated pliers to avoid a shock. If all is well try one short spray of starting fluid into where the air filter goes and try to start. Hint don't use more then one short spray, this fluid burns very hot and can damage you valve seats and piston rings. And always check engine oil level before starting any internal combustible engine

*** note that "hint" it is a more than a hint, if you don't, you will only do it wrong once.

Is it pulling OK, are is there too much pressure, not sure of your unloader type, but many require the trigger to be pulled back when pulling on the starter rope.

As noted will it start for a "moment" if you use starter fluid.
How long as it been since it was started.
** and of course as everyone knows, never start or run one without water going though the pump.