So I was on my way to work yesterday and the battery light came on, and stayed on. I've had quite a few problems with this car, especially with needing to jump start the car about 5 times in the past year, and it wouldn't turn over last week so I had to charge the battery. Naturally, I pulled over and called my dad. He said to just go to work and hope the car doesn't die.

I continued on my way(about 8 miles), and as I went little things started to go wrong. For one, my windows and sunroof would move VERY slowly, and I know that means the battery is dying. Point being, I got to work in one piece, but the infiniti wouldn't start after that, or it would start but you could tell the battery was about finished.

We bought a new battery for it today, and it starts right up, but the battery light on the dash is still on. I drove it from my work to my house(about 20 miles) and it drove fine. Is it safe to drive despite the light on the dash, or should I take it in?