I had the same issue but do not have the automatic climate control but have the the manual controls. Changed the blower motor resistor and no change. Checked all the fuses-no change, The problem was the IGNITION SWITCH where the key goes into the steering column! Do as search on the forum which is how I discovered the problem and how to replace it. What happens is that most people including myself don't turn off the blower motor speed control before they start and stop the engine with the ignition key. The ignition switch in the steering column has all the current from certain accessories running through the ignition switch. The contacts in the ignition switch module spark slightly every time this sequence occurs, carbonizing the contacts over time, eventually resulting in the prevention of the current flow-thus no blower speeds. The ignition switch issue is a fairly common problem on these cars and I am surprised no one else suggested this resolution.
Someone on the forum or the internet had a step by step procedure on how to replace the ignition switch in the column which I followed after purchasing a new ignition switch from gmpartsdirect.com for about $80. It's a relatively big job since you have to take the column apart and get it all back together, Not bad but really not for a novice. You can also remove the old switch, take it apart, and lightly sand the contacts to clean them which I did on my old switch (still have as a backup) but did not use. After all the labor involved, put in a new switch. Problem solved and been perfect for the last 3+ years.
Hope that helps!
