Mac Mini not booting issue
Sounds like a hardware issue. Insert your OS X CD and follow the instructions below from the Apple support pages to test your hardware


Locate your 'Applications Install Disk 2' disk which came with your computer
Insert the disk into the computer
Boot/reboot the computer, holding the D down on your keyboard.  You should get an image like this once the test software has started to inspect your computer
  
When the process is complete, select your language and click the right arrow. If you aren't using a mouse, you can use the up and down arrows to select a language and then press the Return key.


The Apple Hardware Test console appears. You can choose which sort of test or tests to perform:


To perform all of the basic tests, click the Test button or press the "T" key or the Return key.
To perform a more thorough diagnostic test, select the "Perform extended testing" checkbox under the Test button before you click the Test button.
Your test results will appear in the window in the bottom-right of the console.


The Hardware Profile tab of AHT provides specific information about your computer. To see this information, click the tab, then select a subject area on the left.

To exit AHT, click Restart or Shut Down at the bottom of the window. Remember that clicking Shut Down will not automatically eject the disc.



Normally these are caused by hard disk failure, or at least a failure to boot from the hard disk.  If it turns out that it is the hard disk, you will need a new one.  But you may still be able to salvage data from the old one after you've replaced it.  If you get a USB hard drive caddy you can plug the old disk into your Mac after you've reinstalled the OS and if it is readable, you might be able to recover your data.  You may even be able to use migration assistant to recover everything if it turns out that it's just your boot sector that's corrupted.