Do you have proper posture and a chair suitable for your stature? I'm sure the answer is yes, but a chair with a base too deep or too shallow could easily cause numb legs over an extended period of time.
I have tried different chairs and postures without success. I teach yoga classes a few times a week and I see a lot of people (age 40+) showing similar symptoms: numb legs and arms, lower back pain.
I believe an additional problem is that if you sit the whole day the muscles at the front side of your body get too short and the back side too long. So when you finally exercise this imbalance may cause even more problems.
You've wrongly simplified. The knees and hips bend in opposite ways when you sit. Sitting will not stretch the hamstrings, which are on the back of your body. It will stretch the quads, which are at the front.