P0502 Vehicle speed sensor low input
The vehicle speed sensor for this vehicle is the OSS (output speed sensor) without this signal you can expect a hard shift. What this sensor is, is a permanent magnet generator that produces a AC voltage which the PCM then converts to a digital signal, If the speedometer is not working you have a vehicle speed sensor problem, this is not going to be a TPS sensor and yes the TPS is a common failure for the Chevy product.The proof that the speed sensor is the problem is when there is no Speedometer reading. This is also used for the ABS system and Trac to know how fast you are moving. So ABS and TRAC are disabled. When it comes to a AC generating sensor such as the OSS the first step you did was right you replace the sensor, this gives you a good ground to diagnose on. If the speed sensor did not fix the problem you move to the electrical problem, and the PCM.
Here is a Dodge Neon with a famous VSS code P0501. the principle is the same for a Chevy cavalier the only difference is that this is more analog than digital but the diagnosis for the transmission is the same for the Cavalier
So far most forums say the the cause of a non operating speedometer for a Dodge neon is the speed sensor and the pinion gear. What you do not hear is . what if it is the transmission. The speed sensor here is not the problem and it works fine, the pinion gear is not the problem, The way the transmission was diagnosed is, the use of a finger, with the wheel lifted off the gound I stuck my finger inside where the speed sensor is to feel the drive gear, and in a Cavier its the vane gear, with wheel rotating for the Dodge Neon the gear that drives the pinion felt broken just by feel. So in the Dodge Neon case, the transmission is at fault. what drive the speedometer pinion is a plastic gear in the transmission I can feel it wanting to move with the wheels turning then stopping then turning as my finger is in the transmission feeling for the gear, conclusion it is the transmission, plus I can spin the speed sensor with key on engine off and the speedometer starts jumping around.
This is how the shop will determine if this is a tansmission issue, with the wheel of the ground can they feel the vane turn? With the wheels spining by hand. My experience with the cavalier transmission it was either the issue with the speed sensor or the PCM. I never seen a broken vane for the transmision on a Cavalier.