You can try to boot it into Target Disk Mode by holding the 'T' key when you turn it on. Keep holding the T key for at least one minute, or until the Firewire emblem appears on your screen. If that works, then you can connect it to another Mac that has a Firewire cable.
If you don't have another Mac or it won't go into Target Disk Mode, your only option is to remove the hard drive and put it in an external enclosure to back up on another Mac.
HOWEVER, first try a few things before going to all this trouble.
Have you made any modifications to the computer, such as putting in new RAM modules?
1. Press and hold the Option key and turn the power on. Keep the Option key pressed for a minute or two. If the computer boots, use the arrow keys on the keyboard to choose your Recovery partition for booting. If that boots, then launch Utilities > Disk Utility and repair the hard disk.
2. Unplug the Mini and press and hold the power button for 10 seconds. Plug it in and see if it boots.
3. If neither of these work and you have an internet connection, press the 'R' key and turn on the power. Keep the R key pressed and within 3 minutes you should see a recovery boot over the internet. If you don't see it by 3 minutes it probably isn't going to work.
"Raw" is not an acronym, abbreviation, nor a proper noun; thus, it should not be in capital letters.