2002 Chev Tahoe ac is blowing through defroster vent only not blowing through dash board vent

There is a mode door in the plenum box with the heater core and fan. This door can come loose, break, get jammed or the actuator motor for it can fail. Look under the dash for the box and see if you can check the connections for motion when you change the mode.

Being a 2002, the actuators are not vacuum operated. They are electrically operated, however they are difficult to get to. The only one you can get to without taking the dashboard out is the driver side temperature control actuator. Removing the dash on 1999-2006 GM Truck/Tahoe/Yukon/Suburban is quite an ordeal and I would recommend watching some YouTube videos and doing some research before beginning. The part itself runs around $80.00, but getting to it may make taking it somewhere worth skipping the aggravation.

Look for a cracked or deteriorated vacuum hose on the engine.