What is causing shaking and low grumble also loss of power?

What is your question?

This is a 2002 Ford sport explorer Trac 2 door hatchback. The battery was completely drained so I got a jump. Now even after a week of driving it still acts like it doesn't want to start. It has been shaking alot exspecially with the AC on. I also prior to all this noticed the engine shaking under the hood. And when I'm diving there is like a 3 to 5 second shouder now and then I can't explain plus the lights are kinda dim what could be going on?

What makes this problem better or worse?

When I put it in neutral it helps some.

How long has your 2002 Ford Explorer Sport Trac had this problem?

A week