Try with official firmware if you have any PSP games
You don't want the latest firmware 6.61 anyway though you want the firmware just before it 6.60, then either Pro-C with fix 3 or the latest ME CFW for 6.60
6.61 was just a last attempt by Sony to block exploits nothing more
I never had much interest in connecting my PSP to my TV even less so as I own a Playstation TV that is soft modded and plays Vita PSP and PSX and any homebrew only real issue is the price of the memcards that there are no 3rd party versions of that I am aware of.
EDIT it seems there are Micro SD to Vita converters now, I will have to get a couple now
