Q: With car off, exterior and interior lights start flashing

The battery in my car was replaced just less than a year ago. I had gone home during the day for a couple of hours and when I returned to my car the headlights and tail lights were flashing, plus the interior lights in the car cabin were also flashing. I tried to start the car, but it would not start. The radio and windows were working, along with other things in the car, but it would not start. When I turned the ignition, it sounded like the electronic fuel pump was engaging, but when continuing to try to start the car, nothing happened. Also when I try to start the car, it does not have that usual clicking noise you usually hear; there is only a humming noise. Later, the exterior and interior lights stopped flashing. But every time I open the driver’s door and when I turn the key, the lights start flashing again. The headlights were not on when I turned off the car. I found that the battery post’s positive cable was extremely loose. I tightened it and jump-started the battery, but that did not help the problem. What is causing this problem in my car?