How to find a break in the ground wire

If you have power at the breaker, and no power at the room then you have a bad connection somewhere in between. Time to start tracing wires and opening up junction boxes and outlets to check connections - or to hire an electrician to do that for you. There really isn't a "simple, quick" way to do this.

You may find a somewhat overheated looking connection along the way, or more than one, or you may find an actual broken wire, or you may find a wire that is has power on one end but not on the other, and thus broken (or chewed through, or nailed/screwed through) in the wall; though you should always check to see if you might have missed a junction box in that instance.

Assuming you are in north america: In a home wired up with armored cable, otherwise known as BX or AC cable, the armor is the grounding conductor. It is always terminated to a metal box with a cable clamp that secures the cable and completes the connection between the box and armor. The metal mounting bracket(called the yolk), which is the frame of an outlet, is not only mechanical but also serves as a ground conductor for the outlets ground prong(s), the grounding terminal screw and the cover screw. The ground connection is made in one of two ways: via the ground screw or the mounting screws which secure the yolk to the box. The yolk method is acceptable in armored cable systems.

Newer MC or metal clad cable looks exactly like armored cable but has its own grounding conductor. In that wiring system, the armor is not listed for grounding and the wiring methods are similar to that of terminating non metallic cable (aka romex). Meaning, the ground wire must be connected to the metal box, the outlet, and any other grounding conductor.