I've used one of these deco vases as a holder for feeders for my angler, but I wouldn't want to try it as a salt tank. In that small a volume of water, when something goes wrong it is really going to go wrong fast.
The stock filter is fairly weak and it has to be primed to start pulling water. I had one burnout when the power failed during the night and it ran dry since it couldn't start the flow again. If the pump isn't running at all it may already be burned out. If the motor is humming but water isn't flowing try adding some tank water to the filter. If you get the level in the filter high enough it should start pulling water on it's own.
I'm going to have to go with Travis, If you are new to salt, I would take it back, spend some time reading and visiting the forums and get a good picture of what kind of setup you want, then get the gear and get started. Take your time and be patient, as a wise person on one of these forums said, nothing good happens fast in a reef (or saltwater) tank. I would also recommend that you get the largest tank you can afford and support. The larger the water volume, the more forgiving things will be when you make mistakes.
HTH