Since you have another mini, put the bad one into Target Disk Mode (TDM)
Connect a Firewire (FW) cable between the two.
At this point you don't have to shut either down to connect the FW cable. The hard drive on the one you put into TDM should show up on the desktop of the good one as a yellow icon.
Open Disk Utility and run Repair Disk on the bad/TDM hard drive.
Next download the 10.5.8 combo update
from the good mini and then run it on the bad mini. When you launch the installer choose the hard drive from the bad one, it will have the yellow icon.
You won't lose any files or data BTW.
When you're done running the combo update either eject the disk of the TDM machine and disconnect the FW cable, or shut the working one down then disconnect the FW cable.
Push the power button on the bad/TDM machine to shut it down and get it out of TDM/
Boot up the bad one and cross your fingers toes and anything else you can.
If it boots up run Software Update a few times as it will overwrite some system files.