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 there.
It's easier to shiny hunt with the Poke Radar. 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, use a method called "soft resetting": save then initiate battle. If it's shiny, well done. If not, turn off the game to go back to your last save. 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 -- the usual 1/8192 chance shyrockets to a 1/2048 chance.
Hope I helped!
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