Hello. The following is a generic procedure to check and diagnose an outboard motor. If you follow this, you should be able to find your problem.
The first checks to peform are a spark test and compression test; these will rule out an ignition problem and a serious mechanical failure. To do the spark test remove the wires (one at a time) from the plugs, find a good source for grounding on the engine block and hold the metal connector end (under the boot) about 3/8 to 1/2" from the block using something insulated (like a wooden clothespin). Sometimes it is easier to use a 1/4" bolt in the connector to extend it. Crank the engine and ensure that all cylinders have a bright blue spark that easily jumps that gap. This test can also be done with a timing light (inductive is easiest) or a spark plug tester which plugs between the wire and the plug. I know you did a quick test on one cylinder, but it is important to test them all using this procedure. One cylinder missing spark is probably a coil, but all out would point tothe CDI box.
For the compression test, remove the spark plugs and put a compression tester into each cylinder and crank the motor for about 5 seconds. The compression should always read over 100 psi with a variation of no more than 15 psi between the highest and lowest reading cylinders. If the readings fall outside of this range then there is a good chance you have significant physical problems and should have the motor checked further by a qualified mechanic.
If the spark and compression tests are good then you can assume that the fuel system is where the problem lies. First check that you have good new fuel and not contaminated old fuel; modern fuels only have a shelf life of a couple of months before they start deteriorating so if you are using last year's fuel this can cause problems. If the fuel is good then the next thing to check is that all fuel lines up to and including the engine are in good condition with no cracks ,splits, or poor connections. Change the fuel filter - it can block and restrict fuel flow - and check your fuel pump diaphragms since any splits or holes will cause an engine to run inefficiently - it will not pump fuel and if you have a hole in a diaphragm the fuel will usually pass straight into the crankcase and "over fuel" the engine, since most fuel pumps are vacuum driven directly from the crankcase pressure. One quick check is to pump the bulb in the fuel line when the engine is misbehaving - if that improves things, that is an indication that the fuel pump may be a problem. Assuming this is a carbureted motor, if all these checks are OK then move onto the carb(s), which will need to be removed, stripped and cleaned. If you don't have good mechanical skills and the correct tools (including compressed air) I recommend leaving this job to a qualified mechanic. Depsoits are quite common in the carb due to the ethanol in the gas combining chemically with moisture to form gummy solids. While the carbs are off check the Reed valves on the inlet manifold for cracks, breaks, and even a reed missing completely. The reed valves are to help control when the fuel is drawn into a cylinder; if one has broken you will need to investigate to ensure that no internal damage has happened to the engine - this will usually show up on the compression test with an abnormally low reading.