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If the lights go dimwhen u try to start recheck your ground connection .or both terminals .. You may have a bad connection somewhere. Try jump starting .
With an immobiliser problem your car still cranks. Easy check with your key in the ignition the security light shuold go out. If the security light still flashes with the key in the ign then its immobiliser.
The 3GS uses a smart key. If the remote battery gets low you would need to put the key against the start button. Not sure if that's your issue, otherwise try the 3GS forum