First test is to boot from your recovery CD. Put the CD in, and then restart the computer, while holding down the 'C' key. If it boots off the CD, at least some of your hardware is working.
Problem is, the Mac restore CD has no file manipulation functions - even though it should... So your next hurdle is to get a qualified tech to boot the 'puter with a Linux CD - (s)he can then recover your data to an external hard drive.
Another option is to have a tech remove the hard drive from the Mini, and connect it to another Mac, using an adapter kit. Even if the hard drive won't boot, it may still be possible to read it. This has to be done with another Mac, as the Mac file system is not very compatible with Windows computers.