I'm picking this up from our comments. So this isn't a GFCI. Although if it's in the kitchen, and isn't protected by an upstream GFCI receptacle, and isn't protected by a GFCI circuit breaker in the panel, maybe it should be a GFCI.
Did the old receptacle work at all before you removed it, or had it stopped working completely?
Was the hot-side (darker colored terminals) tab removed on the old receptacle (or were both removed)? I suspect not, since your breakers aren't tripping, but worth noting anyway.
One black/white pair in that outlet box is (99.999% certainty) going to be power coming into the box, and the other pair will be power feeding the other outlets that went dead when the new receptacle was installed.
If the tab(s) on the new receptacle are removed, then power can't feed through to the downstream receptacles.
Personally, I would "pigtail" the black, white and ground wires in the box so they feed straight through to the other boxes without going through the receptacle, then you only have to connect one each of the black, white and grounding wires to the new receptacle.