2005 Chevy trailblazer 4 x 2 will not go into reverse or drive

If all the linkages are intact and no solenoids or sensors are bad then I'd say it's toast , How many miles on it ?

If you have lost both forward and reverse then chances are very high that the transmission is shot. Smell the fluid, if it smells burnt then it’s shot.

Answer not posting

Check the transmission fluid level too. If it's good then you'll need to visit a reputable transmission shop for diagnosis. Transmission repairs are usually not cheap so at this point the vehicle might not be worth fixing. Jim