Small Engine Troubleshooting Problems? Ask a Mechanic Now.
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The FB460 has an igniter on it that controls the spark or tells the ignition coil when to spark. It sounds like the igniter has gone bad. Since it won't even fire up when you spray it with starter fluid.
The igniter is a small about 1" square box on the side of the engine(normally starter side opposite of the carburetor), it will have one wire going to it that leads up to the ignition coil. It is most likely that this igniter has gone bad and will need to be replaced.
That is what I have seen to be the problem on those engines most often when you start having starting issues with it.
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On this engine they refer to it as a condenser part number 21013-2064.
I am including a diagram that shows a picture of it, it does look like it may have changed shape from some of the prior ones used on these engines.