You want to write a program in Java that switches the PC on at a certain time, when the PC is off? That's impossible. You cannot run programs when the PC is off...
PCs have a clock chip on the motherboard, and on some PCs it is possible to make the clock chip give a signal at a certain time to switch on the PC. You'll have to set the switch on time in the BIOS settings.
When your PC starts it shows a short message that tells you which key to press. Usually it's F2, but it depends on the motherboard and BIOS. I've also seen F1, Del and Esc to be the key to open the BIOS screen.
Please be very careful when you change your BIOS settings. Your changes may cause problems if you do not know what you are doing. Always consult the motherboard user manual, and if possible get someone with proper knowledge about computers assist you (or do it for you). When in doubt turn to professionals.
As I wrote before, some motherboards have a "wake on a specific time of day" feature.
However, this is highly dependent on the brand of the motherboard of your computer. Some computers have it, some don't. And if you do have a computer that has it, then I'm not sure if it's possible at all to set the wakeup time programmatically. It certainly will not be possible with pure Java (you will have to write native code to do that).
You'll have to investigate how the interface works to access BIOS-related information, see for example DMI.
It looks like that program was written in Visual Basic. You'll have to convert it to Java yourself. But I don't think you'll be able to do it without writing some native code (in for example C or C++).