1999 Chevy Suburban Car shuts off!

I started my car, as I put it in reverse, it completely shut off. No power, no steering, no lights, radio, nothing. I put the car in park, started it again. This time it didn't want to start. It finally started and I drove it around for the rest of the day with only one problem. While driving the lights inside, the stereo and the gauge lights all began to "flicker". Then as fast as it began, it went away. I desided to go home but I stoped to pick up dinner. As I tried to start my car again, it didn't have any power. I tried again and it started, as soon as I put it in gear and gave it gas, it died. Lights, windows, stereo all work. The car just won't start or when it does start, it won't drive and dies. We replaced the fuel pump and battery 10 months ago. I suspected alternator. HELP!