The fuel ine comming in to the carb goes in the bottom, return line to the nipple. Just FYI, this has solved problems on a couple skis I have worked on. double check.
Make sure there are no tears in the fuel pump diaphram, <sp> even a small tear or hole will prevent it from proper suction.
Try blowing air back through the fuel line to make sure nothing is in there.
You mentioned water in the tank. If it still has a stock filter, drain it get a new one. The stock Yami one is a filter and a water separator. Very simpe design, gas floats on water, as fuel passes through the filter, water and sediment fall to the bottom. If there was a lot of water in the tank, even if you drain the tank, the filter will hold the water. Now the fuel comming through the filter, even if it has no water comming from the tank, will pick some of that water out of the filter.
Anyway, sounds like the the diaphram to me.
Check that one way valve again, if it works one way, then it is good. probable just a coincidence that that made it work, but if that valve is broken PM me, I think I have a spare.