Bad battery? Starter? Starter Switch?

... Turning the key to start it results in a lot of clicks, like a dead battery. ...
That is so common, you see it in Hollywood movies. Have someone measure the battery voltage, directly at the battery posts. If it holds >10 V while cranking, the battery is fine. Then measure on the cable sides of each connection. If <8 V, remove terminals and clean w/ a battery brush. Re-attach and spray anti-corrosion on them. This is an annual chore in eastern states, and if your Texas is Houston, you ain't really in the West despite the drugstore cowboys (I used to live there).