Jewell, I was able to find online what the requirements for the Texas state safety inspection are. From recent experience with a car hauler trailer I lost the title to and have owned for about 25 years, I gained a lot of experience.
For the title I will have to take the car to the police station where they will check the vin number and put it on a form which will be given to me. Then because insurance is required to get a state inspection sticker, that's next. Then the inspection where I will get a form showing that it passed. Then the County Tax office where they will give me a lot of negative attitude and reasons why they can't give me a title. Be patient and persistent. Hand them the Bill Of Sale where you bought it, the inspection forms from the state and the police department. AND, in Texas you must have proof of the year it was made and the brand. If they still wont give you a title and tags, go to a County Judge, present the paperwork you have and ask for a Court Order, ordering the County to give you title and registration. It gets aggravating and you will want to call them a few names, but it can be done.