Likely the kernel you're using is lacking support for the hard-disk, the disk controller, or both. Stock kernels, like the ones that come pre-made with distros, usually enable the most popular hardware. If you have something new or exotic it's not going to have support unless you build one specifically.
The other thing is the root filesystem, which is likely ext2 and already compiled in. If you have another live linux system, download a new kernel source and compile it with the support you need. Just trying to get the thing to boot, you may want to enable almost all of the disk controllers and hard-disk options, leaving out all the extra and fancy stuff. Once you get a successful boot, you can look at the screen and see what thing you where missing, then go back and only set that one thing for you production kernel. I went thru the same thing with a PDC20246 controller. Same error message, drove me crazy.
Whatever the computer in question is currently running, look in its hardware info section and try to see exactly what's inside it, then make sure that support is in your boot kernel.
It might be some or any of these (or not
CONFIG_BLK_DEV_VIA82CXXX (grep'ing for VIA