Woohoo! That's a fine looking spark. Let me ask a few questions: Are all the sensors and wires hooked up to the new e-box? Including the white wire to the ign switch and red button? If so, it sounds like you had a bad ignitor box in your e-box. It's nice to have spare parts, but the other bene is you've checked all your 'no spark' conditions except the magneto and validated that they all function as designed. If not, I suggest you hook one circuit wire pair at a time back to the e-box and check for spark each time.
Presuming all the wires are in where they belong, we now move on to water and fuel. Look on the top, and around the water piping for something that looks like a hose end(bib) with a plug in it. Might be white plastic, or blue, or black. It'll have knurled grippy ridges on it like a plastic hose end that hooks to the water spigot outside. If you have this, and many do, this is your shore rinse connections. You can simply take that plug out of the hose bib end and connect your water hose up to it for cooling/rinsing water before we test run.
As Jesse says, if you get impatient, you can squirt a bit of carb cleaner in the spark plug holes, put the plugs in and it will fire for a very short run. this just validates you have spark in the hole and compression.
As for fuel, since you don't know the condition of any of the lines, or vapor return, or if there is a priming bulb or anything else, make sure you have a fire extinguisher handy for the next bit of work. Lets assume the fuel system is copacetic because you found two definite faults with the electronics and the seller didn't mention anything about the fuel system.
You will see three hoses coming out of the fuel tank. One is for regular fuel flow to the carbs from the "on" position of the fuel selector, the other is from the "Res" position of the fuel tank, and the last is vapor return to the tank. There may be a vent at the top, or down where the fuel filler is and it should have an anti-siphon valve in it to protect water ingress.
A word of warning here. The fuel that is in the bottom of the tank, is in the 'reserve' area. Quite often that fuel is filled with grit, sand, gunk, and you absolutely don't want it going through your pipes, and carb. Yes, there is a filter, but it's best not to run that gas in the reserve part of the tank through the engine. If you can locate the reserve line, it might even be labelled on the line as "reserve" or have an "R-1", or "R-out" printed on it. Remove that line from the fuel selector valve, and dump the fuel into a container. Maybe put a quart of fresh in there, shake the ski a bit and dump that too. I've found some pretty sour crap in there and just when you need reserve fuel, if it's gunky, that'll stop up the ski and you have a real job cleaning out the carbs. Once done, put the reserve line back on the fuel selector switch.
Next, locate the output of the fuel selector to the carbs. You can work backward from the carbs, and it's best to take off that large gray fire suppresor on the right side. Once you have that line located, look and see if there is an oblong squeeze bulb in the line. This is a priming bulb, and all Yamahas have them from about 1993 on. Some Kaws have them, some don't. If you don't have one, no prob, you can pressurize the fuel system with -- your mouth!
I don't recall if the oil tank has oil in it or not. If it does, pinch off the line from the tank to the carbs with a forceps or similar. We don't want to be pumping a bunch of oil into the engine as we are going to pre-mix for now. There may be some debate on what ratio to use, but we'll be conservative right now and use 32:1 fuel to oil. If you have synthetic 2-stroke oil, don't use it yet, it mixes at higher ratios but the ski hasn't run for a long time and I want to keep lots of oil on the cylinders, and in the crankcase.
This ratio is very easy to remember, and you can't go wrong with pretty much any of the dino based 2-stroke oil. I'll be straight up with you, I run 2-stroke oil from WalMart in my Kaw, and Yamaha, and never had a bit of trouble with oiling until my son's friend jumped the Yam at full throttle and over-revved it. You pick whatever dino oil suits your fancy. Might as well buy gallon jugs, cause you're gonna need it next summer.
1 oz per quart, 4 oz per gallon, 20 oz per 5 gal jerry can. Mix up 2 gallons like this: In a clean 5 gallon jerry can, pour in 4 oz of 2-stroke oil. Now, fill with 1 gallon of gas. Put the lid on, and shake it a bit side to side in a swirl. Add 4 oz of 2-stroke oil, and fill with the next gallon of gas. We do this to distribute the oil evenly in the mix. If you have to pour oil into sitting gas can, insure you shake it well. Agitate it plenty before pouring into the ski.
Pour the two gallons of pre-mix into the fuel tank. Put the fuel selector to "on". If you have a priming bulb, start squeezing it until it gets good and firm. If you don't have a priming bulb, take a deep breath and blow into the fuel filler for a while. You need to get the fuel into the carbs before it will draw into the jets and fire the engine. Pull the choke knob all the way out, check the carbs and the choke plates at the top of the carb should close. Put the lanyard on the stop button, and push the green button. If you have a water rinse line hooked up, start the water and just let it run. If the engine fires, push in the choke about half way, and rev it to keep it running. You WILL see blue smoke come out the back exhaust duct. Within 2 minutes, you must have warm water coming out the pee tube where your water sensor was, and you must have warm water coming out the exhaust. If you don't have water coming out the pee tube and exhaust, shut the engine off and look for water inside the ski body.
Advise on how it goes. Check your temp warning light doesn't come on, and your gas gauge reads about a quarter or less.
<edit: the line from the fuel tank will go to a small diaphram fuel pump module, and then to the carbs. There will also be a line going into the crankcase from the small fuel pump module. Sorry, forgot they have a pumper type fuel pump.>
