Car won't stay charged

What is your question?

My car died on me the other day and I thought it was the battery. I bought a new one and it still doin the same thing. It'll crank when jumped off, but has no power. I push the gas and it won't go anywhere, and shakes until it shuts off. When i turn on the lights the dash lights go dim and the rpm meter drops. Could it be the alternator?