Is there any way to start a computer at scheduled time when it is
I know how to start it when it has been put into
Currently it is not possible to start a computer from shut down state by scheduling. To better understand this you should be familiar with how system boots up. System switches on when two lines coming from SMPS get shorted by the power switch on the cabinet. When system starts Bios is first loaded to memory, which boots up your system.
What you are asking is to schedule system power on. This has to be done physically by shorting the two wires from SMPS at a scheduled time. Scheduling system start from hibernate or standby or Wake-On-Lan as said in above answer is the only option available.
Looks like you have to do it through the bios, and it is likely not all computers support the auto start feature mentioned here. I assume you are familiar with Wake-on-LAN, waking your computer up over a network connection, probably not what you are looking for but still worth mentioning. This guy had a computer hooked up to an UPS for the purpose of maintaining a network connection for downloads, appearently some BIOSs' have a feature that enables your computer to power back on after a power outage.