I recently rebuilt my 1992 Evinrude 3cyl 60hp. Well,today I started it up. I put the hose on it. With a quick shot of starting fluid,it fired right up. I let it run for a few minutes,since its the first time I have ran it since rebuild. Suddenly it died. I cranked on it some more,no starting. Pulled a plug to check for spark,nada. But then I sprayed more starting fluid in and it attempted to fire. What gives?

don't use starting fluid, use premixed gas/oil

Sounds like a weak battery giving you a weak spark. Recharge battery and try again without the starting fluid. But Choke it a lot!

If you didnt get the flywheel nut tight, it could have sheared the flywheel key, and now you are out of time.Pull flywheel to see if you are still on the key.

Your engine does not use a battery to provide spark,, It only uses a battery to operate the t-n-t, choke, and starter. Boat Dr, has a valid answer, You might check all three cylinders for spark. If you don't have spark on any cylinder, Unplug the big red connection, (that is the quick disconnect to the helm) and using a remote starter button, try again. If you have spark on all three cylinders, it's your key switch, emergency kill switch or a short in the cord. If you still don't have spark, It will be the ign box, or stator. Highly unlikely it would be the trigger, unless you had an electrical short, But 1st try the flywheel key.......may save a lot of time.

Just as soon as it stops raining,I'll remove the flywheel.

Pulled the flywheel. Didn't shear the key. I reinstalled it and tried to start it,nada. Guess I'll tinker with it some more.

Any other ideas? If not,I guess I'll pull it to the shop this week.

Have you pulled the bottom screw out of the carbs to see if you're getting fuel?

Its got fuel. Periodically it will ignite and a puff will come from the exhaust. And I removed the fuel hoses entering the carb. Gas was flowing. This thing has me stumped. If the boat wasnt covered in snow,I would check all the fuses. Maybe I blew one somehow.
GOD I miss my mercury.

A fuse has nothing to do with the engine starting, except to operate the starter or choke. When the flywheel makes a 1/2 turn, the stator makes around 9.5 to16 volts, that in turn excites the ignition box. Also under the flywheel is a trigger, there is a split magnet on the hub of the flywheel, that split makes the trigger tell the ign box to fire and to which cylinder. So see the ignition is self energised and self contained, When you turn the key switch to off, it takes the power that the stator is making and puts it to ground. Thus robbing the ign box of power. So the fuse tht is under the cowling is there to operate the starter, choke and t-n-t. It is like having two seperate electrical systems on one motor and the only thing that they have in common is that they use the same ground.
so to make a motor run. you need Spark, Fuel, and compression. Without one of these, the engine won't run.

Pulled the flywheel again. There are magnet particles stuck to the flywheel. Looks like they broke out of the center of the flywheel. Could this be part of the problem?

so there are magnets, but some are missing??? or what do you mean by broke out of the center?? sounds like if its missing magnets it will be a problem...

Looks like the magnet in the center of the flywheel is breaking apart.

That's the issue. Not sending the signal to fire.