Q: My 2004 Prius don't want to shift to D or N but stays on N

If this failure to shift into gear occurred immediately after battery replacement, somehow the removal and re-application of power to the shift interlock has caused a malfunction. Check to see if the brake lights come on. The brake light switch is usually wired into the shift interlock and if that switch fails what you are describing can occur. Be sure your foot is on the brake during attempts at putting the car in gear. You can try disconnecting (and re-connecting) the negative cable of the 12 volt battery and see if that resolves the issue. Also, check the condition of the fuses in the shift interlock circuit. Apart from that, were you to request a diagnostic, there is multi-page sequence that a mechanic would run through to pinpoint the cause of this particular fault. It is always recommended to simply follow those instructions in the Factory Service Manual but if you desire an expeditious diagnostic, and a quick resolution, you can just request that a YourMechanic professional resolve this. If you desire that this problem be diagnosed by a certified Mechanic, dispatched by YourMechanic right to your location, please request a park shift interlock diagnostic and the responding certified mechanic will get this taken care of for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.