2005 Suzuki Forenza dash borad lights

My husband used my 2005 forenza to jumpstart a old model truck that had stalled on the side of the road, which caused the alternator to go out. It ended up that I needed to replace my alternator and I also replaced my battery. Since then, the battery light and the brake light icons have been on in my dashboard. Let me note, when I drive it for about 15 minutes, the icons go off. So far, my car is still running okay, but when you start the engine, the lights come on. Any suggestions as to why?