Problems after battery change?

Hi. I was driving my vehicle listed above the other day and the battery light came on. It was driving perfectly fine. I took it to Advance to have it checked, and they put a meter on to test the battery, the alternator, and the starter. They said the starter and the alternator were fine, but the battery was having some issues with its reserve. They said I might need a new battery. The battery was about 4 years old. I got a new battery, and my brother put it in for me. He does some work on cars. The next day, when I drove it, the light wasn't on, but then it came on after a short time. I did some research online and it seemed that sometimes dash lights come on or stay on after a battery change until the car has been driven for a while. Since it was driving fine, I just drove it for a couple days off and on. A couple of times, the light just went off. Today I was idling in a parking lot and the skid control light came on. When I began to drive, a couple of other lights came on--ABS, Brake, and power steering. I lost power steering intermittently on the way home. I was very close to my house, so I decided to drive it home and just go very slowly. I pulled into my driveway and right before I turned the car off, I noticed an engine light along with the other lights. I tried to turn the car back on, and it just clicked. During the ride home from the store, it seemed that there was some sort of a loose connection, because the lights kept going on and off and the power steering kept coming on and off, and the seat belt tone kept coming on. So now it's sitting in my driveway. I looked at the connectors on the battery terminals and they seem pretty tight. So, I guess I have two questions: what do you think the problem might be? And do you think I should try to have it jumped and try to drive to my garage, or should I have it towed? Thank you so much for your input.