Pay the tax online:
https://eservice.dlt.go.th/esvapp/login.jsf
You will need to register before you can pay, and since the website is only in Thai, you may need somebody to help you.
The car must pass the technical inspection beforehand, and that can be done in many places. If the car is technically OK (brakes, suspension, lights, emissions), but the inspectors in the first place will not pass it unless you repaint it, try somewhere else.
Alternatively ask the person, who services the car for you, to take it through the inspection.