Why is my car shaking and stalling?

I have a 1991 Honda Civic hatchback that is shaky and when I step on the gas the car
does not feel like it's accelerating. The other day the battery light flickered and then
the car died. I was able to restart it right away however I thought it was the battery
so I replaced it. Today when I drove it, the car was still shaky and still no power when
stepping on the gas so replacing the battery didn't help. As I was pulling into the parking
lot at work, it died on me again and the lights came on and I was able to start it right away
again. What can be causing the car to stall? I have had lots of parts replaced. The fuel
filter was just replaced 2 months ago. I need to know what can cause the car to, A: Be Shaky
B: Not accelerate when stepping on the gas C: Keeps stalling. Please help.

- Frustrated