I lived in Alaska for over 30 years, where a bad battery can mean the difference between life and death. Now I live in Florida, where the summer heat is just as bad for batteries, and while it may not be life and death here, it can be a major annoyance. If I am in doubt about a battery, I just replace it with the best battery I can find. If I still have a problem, I will attempt to troubleshoot it, and if that is beyond my ability, I will have a professional do it.
Bad batteries can cause a whole array of electrical parts to fail, particularly when the vehicle is being started. Much like bad tires, if you have a bad battery, your car is an unreliable hunk of junk until you replace the battery. Just my opinion, mind you, but it is one based on experience. You REALLY need to rule out the battery.