Is there a way that I can backup my old games and still play them on my PS1 without using a mod chip or breaker pro?
Yes, use the hot swap trick. pretty much prop open your ps1 lid with a paperclip and tape or whatever you so choose, as long as the disc doesn't get caught in it. turn on the psx, with a real psx game. you'll notice it start to spin, then it will accelerate, and then decelerate. upon the decelerate, quickly exchange the disc for the back up. (it should be around the time the sound kicks in for the ps logo with the black background) the game will spin quickly and then decelerate again. upon that deceleration, switch the backup for the original game again. the screen will go black, switch it for the back up again. look up psx hot swap on youtube for further help i've done this many times for my back up of ff7 ( the first disc of my og copy is wrecked)