1. Check the fuse. The radio fuse is located in the fuse box under the hood. If the fuse is blown, replace it with a new fuse of the same amperage.
2. Check the wiring. Make sure that the wiring to the radio is secure and not damaged. If there is any damage, repair the wiring or replace it as necessary.
3. Check the antenna. Make sure that the antenna is properly connected and not damaged. If the antenna is damaged, replace it with a new antenna.
4. Check the head unit. If the fuse, wiring, and antenna are all in good condition, the problem may be with the head unit itself. You can try resetting the head unit by disconnecting the battery for a few minutes and then reconnecting it. If this does not work, you may need to replace the head unit.
If you are not comfortable performing these checks yourself, you can take your Trailblazer to a qualified mechanic for diagnosis and repair.