Make sure you only use gameboy roms. Gameboy color/gameboy advance/nes/snes/anything else will NOT work.
If you're sure that you are using the correct type of roms, and they still don't work, then try it with an other game. Ti-boy is an emulator, and emulators rarely get 100% compatibility. Iirc, Mario Land and Kirby's dreamland are amongst the best supported games on Ti-boy, so you might want to try those out as a test. When they work, then you know that there's nothing wrong with your calculator nor your version of tiboy.

You might alsy want to check if you're running the correct version of Ti-boy. There is a version for calculators with a black&white screen, and a version for calculators with a colour screen. The colour version will NOT work on your b&w calculator, though I don't think it would even get to the home screen then.