Multitude of Problems

My husband drives a 2006 Prius with a whopping 206,000 miles on it. He would like to keep the car since he commutes a long distance to work. The car has been having lots of crazy issues lately. The most prevalent issue is that the battery dies frequently. He has also had several instances of his panic alarm sounding repeatedly during the middle of the night. Sorry to all our neighbors. Yesterday he started the car and was greeted with lots of warning lights. That was the last straw. He drive it to Advance Auto Parts and bought a new Optima 12 volt battery. From everything I have read here an old 12 volt battery can cause all these issues. Now this is when things get really strange. Within an hour or so of changing the 12 volt battery the dash went out along with the backup camera. In the middle of the night the panic alarm went off randomly. Then this morning while trying to figure out the blank dash problem, the car decided it no longer wants to turn off. I found the work around of holding the power button for 3 seconds and then quickly pressing it twice to force it to turn off. I was able to get the dash lights back by unplugging the 12 volt battery. All this seems odd to happen immediately after changing out the 12 volt battery. What are the chances that the combo meter would go out within an hour of the change out? Could something else be going on that is causing the car to act so crazy?