I have a Craftsman 2700 psi pressure washer with a Briggs and Stratton 850 engine (80 year anniversary special addition) . It is about 2 years old and used very little and will not start. I filled it with fresh fuel and checked the oil. I also replaced the spark plug and air filter. I checked the fuel line thinking it may not be getting fuel, but there is no obstruction from the tank to the end of the fuel line. I am out of TS options short of taking it to a service center.

Here is the long answer with everything we learned while using a power washer twice a day for years::

It sounds like could be one of the problems listed below or a combination of those things.
1) The exhaust is partially blocked. Check the screen covering exhaust port for carbon and dirt build-up. High-speed exhaust air must pass freely. We finally broke the exhaust screen out with a screwdriver to get our machine going one day.
2) Gas is not flowing freely to carburetor > under gas tank, find the rubber hose connected to carburetor. Pull off rubber hose and make sure gas flows freely. You can use this hose to drain gas tank of old gas ... and then put in fresh gas.
3) Carburetor is partially gummed up and engine cuts off when gas flow slows down. Buy some gum out, and then don't store power washer with gasoline in the tank. Or put additive in gas when storing machine.
4) The choke is letting in too much gas or not enough gas. Try different adjustments. The choke-lever on our power washer got so bad that we could not set throttle at full open or the machine would die. We still use the machine at 2/3 throttle, and then start it each time using WD-40 as described below.
5) Dirty air filter that won't let engine breath enough air to keep up with combustion. Take off air filter and see if problem persists.
6) The spark coil is going bad?? Change spark plug to see if problem persists. Is spark plug wire pushed all the way onto the spark plug?

Now the nitty gritty: we're gonna start that thing right now
7) Take off air filter. Spray WD-40 directly into carburetor. Yes, we use WD-40 every time to start my power washer, and we use the washer twice a week.
Spray in the WD-40, Pull the engine cord. The engine will fire on WD-40. Guaranteed.
Once it starts, keep spraying WD-40 directly into carburetor to keep engine going.
If engine will not fire and keep going on WD-40, then your spark is suspect.
If your engine fires and runs on WD-40 but dies without it, then your gas supply or carburetor are suspect
8) Carburetor problem >>> try Gum out >>> and then take machine to small engine repair shop
9) Spark ... take out spark plug. Put spark wire back on. Hold spark plug by spark wire. Touch metal threads of spark plug to metal opening where plug came out. Metal to metal. Pull back start cord and look for spark between the metal.
If you have no spark, then spark coil is bad >>> take machine to small engine repair shop

Let us know how it comes out!!