How do I allow the roof on my s4 conv 2004 to be put up or down whilst the car is moving

personally I would never open a convertable while I am moving, that is just asking for damage/rips. But if you really want to do this, I would contact the MFG dealer and ask them.

I don't think it can be done. My Chrysler Sebring was supposed to allow operation of the top up to 15mph, but in reality over 5 mph it was locked out. Again, this is not a smart idea anyway, you will likely damage the top putting it up or down while moving. I wouldn't mess with this one.

In my '96, if I was at a traffic light putting the top down and the light changed, I'd release the parking brake, then pull it back up just far enough to engage the "BRAKE" light in the instrument panel. This fooled the car into thinking the brake was still on, allowing the top to continue to function, but not put any appreciable resistance on the actual e-brake. I don't see why this wouldn't work in your car. The brake switch in the emergency brake lever housing seems to be a simple way to determine if the car's immobile, so it's likely they still do it this way. Good luck.