jEnesis is horrible. Which version do you have? Mine decides to go to PAUSE mode on its own for no apparent reason. Also, it cuts the screen, which I don't really like, because teh scaling methods it has are awful. Maybe I have an old version.
As for GBA games, you should get a cheap GBA flashcart (I got one for 9 dollars on Dealextreme) that you can even flash with the DS itself, it's perfect! I also dumped my GBA games to files using the DS. No need for retarded readers, USB drivers or anything!
While on a GBA spree, get the Pinball collection, which has Fantasies and Dreams. it's not pixel perfect but it's pretty good nonetheless.
And if you have a PSP, GBA emulation is pretty good and you can enjoy the same games