rear defrost problem

Hi all, I got that 2001 cavalier and I am having problems with the rear defrost. It started with no heater fan at all after a smoky smell. I found a shorted power wire at the panel's rear connection, behind the A/C rear defrost plug. I replaced the connector and the control panel and got back the heater, A/C and rear defrost.
Now, the problem is that when I turn on the rear defrost, everything is working fine, but as soos as I turn on the head lights, and the panel lights at the same time, the rear defrost quits after a couple of seconds and the heater's panel lights also turn off, but the head lights and other dash lights are ok. I turn off the lights and turn them back on, and everything lights up until I turn on the rear defrost again.
What is common to both of those?
Thank's, Martin