Transmission woes

I have a 2006 Chevy Trailblazer with 144000 miles. While trying to pull out at a stop sign the transmission would not shift into gear. The RPMs went up but it did not move at all. I shut the vehicle off and let it sit for a minute, and then it worked fine for another 5 min, until the same thing happened. I had the car towed to my house, as it arrived I got in it and drove it right into its parking spot. all gears worked fine. after parking it i put it in drive and once again the car would not move, just an increase in RPM with no movement. Long story short, after running for a minute the truck will not shift into gear, after letting it sit for a couple minutes (not even enough time to cool down) it works for another minute. It seems like the computer may be cutting it off, to prevent damage, but I don't know why. I have talked to a few people who say they have had the same problem (Trailblazer wont move, after cool down moves again) but mine seems to work again shortly after shutdown. It will shift through all the gears when working including reverse, until it stops. then nothing. Ive never had this problem where as long as its working its fine, but cuts off until you restart car. It will not work immediately after shutting off it does take a few minutes, (5 tops) no where near enough time to cool down, also it goes out right after a minute or two of use not enough time to get hot.. Any help would be greatly appreciated.