Hi
I am a certified personal trainer.
If you do enough cardio for it to be effective in terms of fat burning, you are burning first the glucose that's immediately stored in your muscles, then the energy stored in your liver, then fat. At that point, unless you eat a meal and rest for a while, you don't have enough energy left to do a useful weight workout.
A 5-10 minute walk, bike or elliptical warm-up before you do your weight workout isn't going to deplete you, but 30-60 minutes of real cardio should use ALL the short-term energy stored in your body. That's the energy that you draw upon when you lift weights.
Very fast paced circuit training, where you incorporate bursts of cardio between sets of weight training is another way to completely deplete your energy reserves as long as your primary goal in lifting isn't muscle building.
Mel