What is wrong with my car?

I'm sure it's electrical engine... My car decided to die one morning and we were able to jump it, however once I reached my destination, it died. I was able to get another jump, however it died about a quarter-of-a-mile later. We thought it was the alternator/battery, so we replaced both ourselves. Doesn't seem to be the problem! We are no longer able to jump it to go, however when we hook it up to another vehicle for a few minutes, it'll turn over but die as soon as we disconnect. When we try to turn it over, it just makes a whirring sort of noise. It's a '93 mazda MX-3 V-4 base model.