If you bought a psp slim and lite to play games on your tv, you will find out that you cant use a standard composite cable(av 3 colors), but you have to use a component(5 cables), and the tv needs to support progressive scan. Well you can still play psone games through your tv, but you need access to a ps3. I tested this at my friends house by hooking up my psp slim to his tv using component, even though his tv doesnt support progressive scan. Then i remote connected to my ps3 through his wifi, and was able to play my psone games, the ones i downloaded and the psone disc that was in my ps3.
so thats how to play psone games on tv without progressive scan or component cable
P.S. if you have a component cable and a tv with progressive scan, you can play psone, homebrew, and psp iso/umd's on your tv, and with composite or without progressive scan, you can still play music, videos, and umd movies, use internet radio and web browser, but u need ps3 for psone games