IF the speedo does not work that means is not getting a signal from the output sensor. Also delayed and erratic and mushy are controlled by the input sensor speed battery level must be correct/ idle...
You will require a "magnetic doughnut" from your local dealership. It goes over the tire stem, then you retrain the pressure sensors though the computer prompts.
Here are the speed sensors!!!.
There are sensors at each wheel that reads magnectic impluses. They can be damaged quite easily and should be taken care od and kept clean.