You can run homebrew apps on a PSP-3000 with v6.31 firmware (it's commonly thought on the internet that PSP-3000 is homebrew proof but that's not the case. You just can't load ISOs on PSP-3000s with anything later than v5.01 firmware. But you can play roms on emulators and do a bunch of other stuff with v6.31. According to the people who take part in the PSP homebrew scene.)
For v6.35, you are probably SOL if the hackers haven't found an exploit for that version yet. I haven't visited those PSP homebrew sites in a couple months so maybe they've made some progress I don't know about.
I haven't personally trying running the exploit for my PSP though (Peacewalker model Green PSP with v6.31. Came with v6.20 out of the box but I upgraded the firmware). That would require me to rent or buy a certain PSP game. I can't be arsed to do that right now. I have like 3 PSP games on hand at the moment that I haven't beaten that I could play anyway.
