Added Dechlorinator, Everything Went Cloudy

The addition of dechlorinator is probably a co-incidence. Cloudy water within a couple of days of setting up a tank is common. Though maybe the dechlorinator did help a bit.

A brand new tank is full of organic chemicals. The plasticiser in the filter housing, in the silicone joining the glass together, probably in something smeared over the glass and so on. There are bacteria which use these organic chemicals as food. They live free floating in the water and multiply very quickly. We see them as the cloudiness. The reason the dechlorinator could have helped is the chlorine would have inhibited their growth at the beginning, though the chlorine would have gassed off after about 24 hours with the outflow from a filter churning the water up. Unless you have chloramine in your water supply instead of chlorine, which doesn't gas off.
The good news is that once the bacteria have 'eaten' all those organic chemicals, they die and the water clears. The bad news is that they are not the same bacteria we want in the filter. They don't use organic chemicals for food, they use nitrogenous chemicals. The water will have cleared well before the cycle finishes, just ignore it.

I recently bought a new tank for my betta. I transfered most of the water, sand, filter and heater from the old tank. I had cloudy water for 24 hours with just the organic chemicals in the silicone and on the glass.