Hello,
Here is how I solved this problem:
There is a power management section in the
BIOS settings of the PC where you can set, among others,
a daily
power-on time.
This only works for the PC's with Motherboards that have this feature and that are supplied by ATX power sources.(
don't worry, this options were introduced a very long time ago, so if you own a computer that is younger than 10 years - it's very likely that you will be able to set this up)
You need to make sure that the PC doesn't ask you for a password and loads without needing input from user (My bedroom PC doesen't involve a lot of security so it's ok...)
Next create a .bat file that contains the :
C:\Progra~1\Winamp\winamp.exe "c:\Music\MyFavouriteMelody.MP3"
line. Custumize with your own player and your own song. Save the .bat file with an intuitive name like MusicStartup.bat
Create a shortcut of this file and drop it in the Start>AllPrograms>Startup folder
And voila : Each time your computer starts up it will load that song and play it.And since you can set the bios to start up your PC at a certain time, every day, you have made for yourself a PC alarm clock.
Just make sure you leave your speakers on, and the bios time and date are correctly set.
Now...
Surprisingly, even though I set up my speakers preety loud(definitely louder than my former phone alarm clock), and the song was a ATB energyc song I had trouble waking up the first morning I tried this...
I figured it was that my subconcious was used to ignore those kind of loud sounds from those late nights I used to fall asleep during watching a movie.

I hope that, with time, I will get used to the new method.
So I strongly advise you to use your old wake-up method for a fail safe...