You say your and old PSP hacking fan, did you try fixing the old PSP with the pandora's battery method?
You will need to use that method if you want to put a custom firmware on the slim also.
Explanation of what the Pandora's battery is.
Guide on how to use the Pandora's battery method. This will create a magic memory stick that can will unbrick/install a custom firmware on both slim and fat PSPs.
You need access to a PSP that can already run homebrew (friend etc) to create the Pandora's battery/magic memory stick.
You can buy a datel 'tool' battery or hard-mod a battery by cutting a pin, but you still need the special files on the memory card.
No-one can legally give you those, a second PSP that can already run homebrew is needed because is can both decrypt sony's protections, and run homebrew code.
With both those things it can modify an official sony update file into a magic memory stick.