I assume you are talking about an automatic transmission. There is something in the transmission called a torque converter which basically senses the RPM gauge and is responsible in changing the gears.

Having said that, unless you were in the vehicle and heard it snap, then it is highly unlikely this is the issue as, they usually snap while the engine is running. I have, however, run into an issue with a different make vehicle that had a fuse linked to the transmission box which blew and was unable to put the car in gear. I would double check your fuses(concentrate your search with the diagrams in your vehicle manual) as one may have blown and you not know its vitality to the car.

Driver's side door fuse panel has a few fuses that may fix your issues.
One will be marked as ERLS-cruise control, engine controls.
Two will be marked as CLSTR-Instrument panel cluster.
the third one will be located on the driver's side under the hood.
Three will be marked as BCM/CLU-body control module\Instrument panel cluster

Hope this helps.

Have you had someone check the transmission speed sensor ?