We need pics of the carts board. The bars on the screen are probably there because the battery in that thing is probably dead and the uploaded graphics are gone. I wouldn't hook that thing up to a PC trying to fiddle, if you also have to upload a ROM to it to run the program, you'll lose all program before you can even dump and possibly reverse engineer the code that runs it, although hopefully you just upload graphics to it. Although I doubt now that it's just the graphics you upload.
Take it apart and take some pics of the board, and hope it's just got bars not from it being run on batteries.
And as for the USB->Parallel cable, I'd not mess with that. You just need an XP tower with a parallel port.