New Shimano TX55 Not Shifting I am having a problem with my rear derailleur. I installed as per instructions, adjusting the H and L limits to what I believe is proper. The problem I am having is that when I am in 7th gear, shifting down doesn't actually shift. The cable tightens, but it just pulls the derailleur back instead of sideways along to the next gear. I have tried both tightening and loosening the cable in various amounts. I also noticed that I can push the derailleur from side to side (as if it were changing gears) while the cable remains at the same tension.

As this is the first derailleur that I have installed myself, I really have no idea whats wrong. Did I install it wrong? Is it broken? I'd appreciate any help.

EDIT Added a newer video that hopefully shows the problem better.

Here's a video of the problem
Thanks for all the help! I had a friend take a look at it in person. Turn out the cable housing between the frame and the derailleur was too short. The derailleur was cocking back until it caught the cable housing, then working as normal. After a replacement with longer housing, the bike is now working perfectly. 

Thanks again to all who helped!