Are the stop lights and turn signals separate circuits, or are they shared?
I don't think the resistor is your problem; that's mainly warranted when the reduced current consumption of the LEDs causes the flasher to flash at the wrong rate (as it would if a bulb were burnt out). It would not affect the brake lights at all. Incidentally, such resistors are installed in parallel with the lights, not in series with them.
I suspect you have some connections that have their polarity reversed (LEDs are of course polarity sensitive, while incandescent bulbs are not) or else a bad or missing ground connection. I may be entirely wrong.
