I know for a computer I can change the BIOS settings to have it 'auto on'. This way the computer turns on by itself after power is restored ( instead of manually having to start the computer after power loss).
Is there a similar BIOS setting or a program which I Can use to auto restart a latop?
I am asking this as a general question as we are planning to buy some cheap dell laptops. So I did not include the make and model.
We have the same situation with a laptop in a remote location. We hook it up to a 2 hour UPS and when it quits during a power outage, the laptop battery is set to go to sleep mode when the battery reaches 50% discharge. In sleep mode, we find it will last for more than a day. A meaningless task is set to run every 24 hours, but only when AC power is on. This task can wake the computer. So, when power is restored to the laptop, the computer wakes up, within 24 hours.
I'm assuming you're using a PC by the way you phrased your inquiry. If so, it depends entirely on the manufacturer of the BIOS, which varies between computer manufacturers and sometimes even between models from the same manufacturer. I used to work for Dell in the Manufacturing Line Support area so I have some intrinsic knowledge of this subject.
Other than going to your BIOS and exploring it for a solution, you can really only contact your system manufacturer and investigate with their support team.
As for auto-resume support via programs, such an application would require direct BIOS support to implement that functionality so I'd wager you won't be able to locate such a program.
I would not expect it to be available on any laptop. Some, but not all, Desktop PCs offer this functionality. Older PCs where the switch actually switched the power is was there by default. Newer PCs may have options which return to state at power interruption (not necessarily reliably), or power on automatically. Modern power supplies usually don't fully power off, but provide limited power for things like the Wake-on-LAN and the power button.
Because of the battery, power disconnect does not mean shut down for a laptop. The laptop will have functions to handle shutting down when the battery runs down. It will have limited funtionality when the power is connected. Mostly this consists of an indication if the laptop has line power or not. The only power-on mode that would make sense on a laptop would be Wake-on-LAN, but that would likely need the laptop to be in sleep mode.