E6430 power problem

I have a Dell E6430 model laptop. Normally, if I remove the battery (it has a removable battery) and plug in the laptop charger, it should power on when I press the power button. However, it doesn't turn on. (Sometimes, if I press the power button after a few minutes, I hear a buzzer sound for 5–10 seconds, then it stops, but the laptop still doesn't power on.)

If I wait for 15–20 minutes and then press the power button, the power button light turns on (at the same time, the Caps Lock light blinks), and the laptop powers on. If I press the power button before waiting 10 minutes, only the power button light flashes, waits 2–3 seconds, and then turns off—the laptop does not power on.

(This happens whether the battery is installed or not. After the laptop powers on, it works perfectly. There are no faulty parts. It runs flawlessly. The CMOS battery is new. There’s no issue with the RAM. The BIOS is up to date. I have also reset the BIOS. The power button is not faulty. There is no issue with the charger. I have two chargers, and both work. The battery is dead. However, this laptop should work without a battery when plugged into a power source (as most laptops do). When the laptop is on and I plug in the battery, and then remove the power, it can stay on for 10–15 minutes. The battery is not important for me.)

Once powered on, the laptop can run for hours without any issues—there are no shutdown problems. It also restarts properly. What do you think is the cause of this issue? Have others experienced a similar problem?