Well, a little late, but.....
Your description is like Deja Vu for me..... Has happened more times then I want to think about to me..... I believe the root cause is often a bacteria bloom from the move (especially if its white cloudy). The bacteria eats all the oxygen, leaving none for your fish. Why the bacteria bloom? I THINK its because the bacteria colony was disturbed, and the normal checks and balances on the colony shifted, allowing one to out compete the others temporarily. Best move? I agree, get a cycled filter. By preference, a sponge filter. And KEEP THE CRAP in the filter!!!!! It looks like dirt and mud, but it has ALL KINDSA beneficial bacteria.
Also, especially when you first notice this happening (it has a lot less effect later on, after things start to stabilize), up the air in the tank as much as you can, drop the water level a few inches, and if you have a spare power head use it to create surface agitation. The surface agitation of the water is what allowed the water to expel CO2 and absorb oxygen. Dropping the water level a few inches creates a larger vertical space for the O2 exchange to take place in. If the tank top is tightly closed, you might want to open it up a bit and place a screen over it to keep the fish in. Again, this aids in the air exchange.
What I do now to help prevent this issue is set the tank up with heavy surface agitation and lots of air stones on the bottom (to create water circulation) for an hour or so before I put the fish in. I know that my own water tends to be light on oxygen, and it can take a little while to stabilize.
Finally, get a dissolved oxygen kit. Plus a pH kit (low and high, even if you only have high range fish), and an ammonia, nitrate, nitrite, general hardness, carbonate hardness, and CO2 test kits. And any other test kit you can think of. These kits can eliminate a LOT of guess work when you have a bizarre problem in your tanks. You might only use them once a year, or not at all, but when you have to tell some one that your fish are acting strange, the ability to tell them what the O2 is, and the rest of the info, can be a priceless advantage in the race to save your fish.
Later!
Amanda.
PS: Love Prime. It locks ammonia as well as chloromines and choline. And does a few other things to boot.