I have a 2004 Chevy TrailBlazer that just developed a problem with the left turn signal. The left turn signal indicator on the dash is blinking rapidly and the tail light turn signal is out. I change out the bulbs and I still have no lights for the turn signal and brake. I also check the fuses and they seem okay. The right turn signal and tail lights are working fine.

check for a bad ground wire connection for the indicator bulb

check to see if security system is working (activeated) ,look at fuses

Check for OBD2 codes, primarily a code indicating PCM memory is corrupt. My Trailblazer at times wouldn't turn over and start. Nothing at the key. When you attempt to start the vehicle and you turn the key to the start position, the PCM sends a signal to the starter relay to start the engine. Youtube video showed a mechanic warming the PCM with a hair dryer, and it would start. Tried it on mine and it started fine. If it is the PCM, the remedy is PCM replacement. Got mine from pcmforless.com about $100.00. They had to program the new PCM with the vehicle vin number. Once installed no more problems.

Probably a short in the wiring harness inside your steering column.

Remove the shroud pieces around the column

There were problems with the circuit board assemblies on the earlier years of the Envoy. Also check the socket for the brake light, make sure the contacts are OK.

Replace left rear turn signal bulb. That "fast blinking" is a built in feature to let you know one of the bulbs (on side that's blinking fast) is bad.

Take the switch for the hazard flashers and jiggle it, ....up and down,..... a lot. Somtimes the contacts get dirty.

THERE IS A BLINKER RELAY UNDER THE DASH. IF YOU CAN GET ONE OF THE BLINKERS TO BLINK YOU CAN HEAR THE RELAY LISTEN CLOSLEY THEY PUT THESE THINGS IN SOME HARD TO GET PLACES

perhaps its the wrong bulb or the bulb isn't incerted correctly, had this problem on my moms truck.