Central Air duct does not blow
Disconnected duct-work, a closed shut-off louver (somewhere in the duct-work, not at the register), or it's the longest and hardest-to-run stretch, therefore possibly undersized to fit in the space or a poor job done connecting it, are all likely culprits. Contract someone who has troubleshooting experience and an inspection camera. Standard duct cleaning service companies aren't likely to have either. Re-balancing the system will not solve the problem as you have tried that already (unless it is a hidden closed louver). 

If I had to guess (if it's not just broken duct-work), it's the longest, hardest-to, smallest diameter run in the house, running in horribly mangled (kinked) 6" flexible. Solution, replace with ridged.