Huge Hesitation - Unmetered air???

[HotRB240]

The car is a 1996 240SX SE with a series 1 RB25DET out of a 1993 R33SkylineGTS-T. Everything is pretty much stock, including the turbo. I payed $800 to have a board wired onto the ECU and then have the car tuned. At high RPM the car pulls ok, not great. In the middle of the rev range when you put the peddle down it just sets there and does nothing. My mechanic said it's showing that it is thin for whatever reason, and he suspected that somehow unmetered air is getting in. Then, the hose that comes out of the right side of the block he saw wasn't connected. The car idles fine, and drives fine when driven easy. But when you put your foot down around 3000 RPM it doesn't do anything. Can you please help me with diagnosis? I really appreciate any ideas you may have. Thank you.