I changed my battery and my car won’t shift out of park.

Hello, the brake light switch is what sends the signal to the shift lever to release he shift lever from the "park" position. If that switch or related wiring and circuitry is compromised, then yes - this could cause a problem. I'd check in this area first. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops