wake-up by the computer
Solution 1:
Most BIOS have an option to wake the computer up at a defined time. This option is usually named "Resume by alarm" or "Wake-up on RTC", something like this (not wake on lan, though, this is something else).
You can find more details about it at this article.
Nb: You can find a list of keys to enter the BIOS setup at this page. It should however be written in a corner when booting the computer.