Thank you for your swift replies..
No, the Computer isn’t that old, it runs more than 3 hours on battery power; however, to find out whether the issue is battery related, I did remove one battery at a time and reverified (It has two identical removable batteries and It works even if one of them is not installed) but it kept restarting. Considering that it is infrequent that the two batteries will go bad at the same time, we may assume that the two batteries are good.
Wake-on-LAN wasn’t actually enabled.