Here's the problem in a nutshell. No pro-level software will be happy on a system with 4 GB of RAM. Premiere will probably run, but Adobe suggests 8 GB as a minimum for acceptable performance.
So, ultimately, my advice for a computer like that is to use iMovie with it. It's specifically designed to run on less powerful systems so it's accessible to more people.
I realize that you've said you are out-growing iMovie, but the hard truth is that your computer can't really out-grow it. I'd suggest staying with it until you are able to replace your computer.
(Remember, you don't have to buy the newest and greatest. You could buy a 4-year old used computer and it will STILL be 2 years newer than your machine. Look at places like Powermax, maybe, and see if anything's in your price range.)