I recently started a weight training program. How can I get a good cardio workout I am constantly sore and have poor muscular endurance?

I must agree with Ricardo that rest is essential. Assuming you've had no training prior to your workouts then the muscles will become naturally fatigued until you start building endurance. You may also want to investigate the use of suppliments such as glutamine, creatine, proteins, together with a good multi vitamin to assist yoiur work out and reduce the on set of fatigue

The HIIT workouts you are describing are to improve strength and muscular endurance. If you are fatiguing, you are not fully recovered yet, no matter what the schedule says. Your body needs more rest time between workouts. Add an extra day between HIIT workouts. Consider using the short time of the Tabata workout, which focuses on improving your VO2 Max or ability to use oxygen, as a workout between HIIT workouts, once or twice a week for two to three weeks. The cardiovascular stress will add to your aerobic and anaerobic capacity, while the short duration and lighter weight used in the Tabata intervals, will allow you to continue with muscular recovery.

Undulation ropes. Increases heartrate and workload much faster than running; makes it much easier to start improving cardio. Otherwise, jump roping is a tried and true method. If you are finding yourself with fatigued muscles, reevaluate your nutrition. You can use vitamin supplements like "Animal Pak" if your workouts are extremely draining. And remember, rest is just as important to the muscle building process as working out. Make sure your muscles are allowed adequate rest to rebuild and recover. Lift too soon and you get dystrophy, too late and they atrophy.