You can check recalls at safercar.gov. Your local Chevrolet dealer can tell you if this Trailblazer has any open recalls. Chevy maintains a database updated by the dealers when a recall is fixed.
A rebuilt dash cluster may be your best bet here to fix the speedo and odo.
As for the AC, have the refrigerant charge checked and go from there.
The blower motor likely needs one of these below. There are a number of different ones depending on the system in your car so order accordingly but they all look like this;
Before I did my stepper motors, a cluster was about $300, then had to get programmed for another $100. 6 stepper motors, $22. Some online places were $60 to $100 to do the stepper motors.
The blower resistor for mine was $20 or so and easy to replace.
If I was you, I wouldn’t just assume the cluster and/or stepper motors are the problem
I’d have somebody attempt to “sweep the gauges” with their professional level scan tool. If the gauges respond correctly, then the cluster and/or stepper motors are not your problem. If they don’t respond correctly, then a stepper motor replacement, or perhaps a rebuilt cluster is the next step
As for blower speeds, it sounds like the resistor pack is faulty
Concur w/DB above, a pro diagnosis is in order. You can fix the problems yourself if you like but money well spent to get someone with a Chevy scan tool to complete the diagnosis and tell you what’s wrong first. One more bit of advice: Repairing AC systems can run into a lot of money. And if you try to do the job too cheaply, skipping steps in other words, it can run into a really lot of money. If you can live w/o AC, that’s the thing to do for now. Summer’s almost over after all. When you decide you need AC, seek advice from an AC specialist shop. Again, something you can repair yourself, once you get a pro diagnosis.
What I find unusual about this failure is that the odometer relies on the speedometer stepper motor to operate, that wouldn’t be the case with the vehicles that I am familiar with.
I would suspect a speed sensor failure but that should result in a fault code and warning lights.
That is good news for somebody, it is going to be 105 F for the next 9 days here. I use my A/C 10 months a year.