The brown wire could be a "hot" wire that separately controls the fan or light. It also might be an unswitched "hot" wire that allows the light to be switched but the fan to continue blowing even when the light is turned off at the switch.

If the brown wire is an alternate "hot" wire, then connecting it to the ground wire of the fan that would cause a short.

In any case, determine which wire is connected to the switch. Use a tester on the brown and white wires to see if the brown is "hot." If so, then switch the switch off and test it to see if the switch is connected to it.

Also test the black wire to see if it is connected to the switch. (Turn it on, then touch the tester to the black and white wires to see if the tester glows. If so, then turn the switch off, then do it again to see if the tester then does not glow. If it does, then the black wire is switched.)

It is kosher to hook both the fan and the light up to the same hot wire coming into the box. That is not the problem.