Your game isn't defective. It's just really hard to get a shiny in Platinum, especially seeing as the Shiny Charm doesn't exist in that game.
It's easier to shiny hunt with the PokeRadar. Encountering the same Pokemon in a row increases the chances of getting a shiny. The chances will still be low, but better than full odds.
For static encounters, save, then initiate battle. If it's shiny, well done. If not, turn off the game to go back to before. Keep doing this until you get a shiny.
For hatching shinies, use the Masuda Method. You take two Pokemon of games with different languages and breed them together. This drastically raises the chances for getting a shiny, as instead of the usual 1/8192 chance, there's a 1/2048 chance. Hope I helped!
Hope I helped!