Where did you buy the game from?
It's possible that you have a pirated game.
If the ds lite loads a ds game, but later ds models don't, since platinum is not dsi-enhanced(meaning jap versions will work regardless of model used to boot it up, meaning not a factor in terms of your problem), the solution is staring right in your face: unlicensed bootleg platinum in your possession when it shouldn't if you want inter-ds activity w/o troubles...
My D/P FC: 4255-0421-2254
My Pt FC: 2450-0507-5436(old)
My HG FC:3524-8966-7093(old)
My black FC: 0691-4324-8351
My black 2 FC: 3440-0907-8860
My Y FC: 4038-6458-7352