Well, the good news is that these little jewels are pretty easy to work on and that goes for the simple carburetor. The bad news MAY BE that you'll have to do the work yourself if you want it done right!
With proper care and, most importantly, attitude, these engines CAN BE pretty much trouble free. After all, they are the best in the world...in my opinion.
There is really no need to have a fuel/water separator for this outboard if you run clean, fresh gas and drain the carburetor before putting the engine up for any length of time. If you do not do these basics, there is no "device" that will counter the effects of poor quality fuel being left in the float chamber. As a matter of fact, I don't like to see these smaller outboards run with water separators as they are usually the first place trouble lurks. If a guy won't empty his float chamber routinely, then he sure as heck ain't gonna keep up with maintaining the water filter. And, having said that, that's where I would start the "hunt" for your no start issue.
"Authorized Honda Dealer" is just that, "Authorized". Not bad, not good, not great. Just authorized. Some ARE great but, I suspect, just as many are not and it's a crapshoot and a crying shame that you just never know what you're getting into when you walk into a business until you plunk down your money and walk out. It's the same all over. Car dealers...truck dealers...computer repair. Some good, some not so good. When your outboard was "winterized", you relied on the dealer to do a good job. Maybe he did, maybe he didn't. But it's up to you to find out now.
It sure sounds like a fuel issue from here and, as I said before, that water separator COULD be the culprit. With those things screwed on to the transom, you have extra connections that can leak and extra hoses that can separate internally and plug.
First thing,
You say that you recently installed the fuel/water separator and fresh fuel. Did you get all the connections "air tight"? It could simply be a matter of it sucking air and vapor locking. Other things that come to mind are:
Is the tank vent open and clear?
Have you cleaned and inspected your fuel tank for dirt/debris?
Does the primer bulb stay hard after you pump it?
Have you tried draining the water separator into a clear container to check for contamination?
Have you tried draining the carb into a clear container to check for contamination?
Have you pulled the spark plugs and taken a look?
Have the plugs been changed recently?
I ABSOLUTELY DO NOT recommend using starting fluid (ether) on one of these fine engines except in an emergency.
But, you can get a can of carb spray and about 2 ft. of vacuum line from the auto parts store to make yourself a little test set up. The engine will absolutely run on carb cleaner with no damage as would occur with ether. Snake the vac line up through the sound muffler and into the carb throat then put the little straw that comes with it in the line and give it a good "burst" then turn her over. If it has spark, it should cough, sputter or run. Then you'll know for sure it is a fuel issue.
One simple thing to try to get her going without a carb tear down is to loosen the carb drain screw and take some WD-40 and, again with the little straw, stick it up the drain tube and flood the float chamber then let it drain. Do that at least a couple of times then take that can of carb spray cleaner and do the same thing. Then close the drain, pump up the primer bulb and then open the screw again and flush the bowl with gas. Then close the drain and try to start. Sometimes it works and sometimes not. If the float or inlet valve is stuck, this can un-stick it.
Good luck and let us know how you're coming along.