look in the bios settings and see if you have the settings for automatic startup enabled or not
BIOS Settings - Some computers support wake on alarm in power management area of computer BIOS.
The only two ways I know of to automatically turn on a computer is the "Wake on LAN" feature, which likely doesn't apply to your situation, and the "Power on by Alarm" feature sometimes available in the system BIOS.
The BIOS settings are those available normally when you first start your computer... a message that says "[F2] to enter Setup" or something similar. Sometime the BIOS access key announcement is hidden, but the access always works. You can check with your manufacturer website for the actual key to use if it isn't displayed on the screen. The more typical BIOS access keys are F1, F2, F10, or the DEL key.
Assuming you make it to the BIOS, the bottom of the screen usually has navigation tips. Look for Power Mangement or something similar. From there you would look for "Power ON / RESUME By Alarm". If that option exists, it'll allow you to set a time for automatically turning on. If it is there, F10 normally saves and exits the BIOS settings, and ESC and then "Exit without Saving" would be the way to go if you never find the feature you're looking for.
Good luck, hope this gives you a direction to look.