NM cable is permitted in conduit. It is even required if the cable is subject to damage.ROMEX should never be ran through conduits - too hot) or THHN Wire thru EMT Conduits.
Ground rods have nothing to due with providing a ground for the 3rd prong. Ground rods are for high voltage events like lightning.What you need to do is make sure your wires are running through a metal conduit (EMT). From there you can put a ground rod outside your house near the Load Center or Meter and make sure it is not less than 6' from any incoming power source such as the Load Center (breakers) and Meter. You can then ground all your metal conduits to that rod by installing a ground ring on the conduit line at the Load Center with 4 AWG THHN wire. Then you can upgrade all your receptacle boxes to have a ground wire (14 AWG THHN is fine for each receptacle) tie directly to the receptacle box for Earth Ground.
Oh the bad side and not having everything running through a metal conduit where you do as above you can run a ground rod and tie that into the neutral block of the load center. In some states that's actually required that your neutral is bonded to earth ground by a Green Screw in all newer Load Centers. Now just twist tie the neutral (white) and ground (green) wires together at each receptacle to achieve proper grounding.
Otherwise going 3 prong without proper earth grounding is pointless.
The neutral to ground bond is what assures a breaker will trip on overcurrent due to a short. This is not just in newer panels or some states.
This is extremely dangerous advise. This is a bootleg ground and can energize the metallic parts of the system and create widespread shock hazards.Now just twist tie the neutral (white) and ground (green) wires together at each receptacle to achieve proper grounding.