this is where the splitter and AC adaptor is located
So you have the AC adapter plugged into an AC outlet...the AC adapter is connected to a short segment of coaxial cable...the short coax is then connected to a splitter. Right?
One output of the splitter should read "To TV" and the other outlet perhaps "To Amp." The "To TV" outlet should be connected to the Mini Box.
If every other device in your home is working fine, I'd suspect the "To TV" outlet on this splitter connected to the Mini Box has become faulty.
If you disconnected this AC adapter and the other 3 other set-top boxes lost signals, I'd suspect there is an amplifier somewhere in your house because I couldn't imagine 2 other splitters daisy-chained off this "To Amp" outlet of the splitter near the Mini Box.
Where does the coax connected to this "To Amp" outlet go? Follow it.