While changing box, it is highly likely that your disks no longer have the same device name as viewed by Linux. This could be because the driver is a different one, or they are just numbered differently. In any case, the disk that used to be /dev/hda may now be /dev/sdb, or something else.
You should boot the new box on a rescue CD (live CD, any distro will work). Then, check how your disks are detected, find their new names, so you can update your configuration.
First, you'll need to update GRUB's config. GRUB does it's best to use "independant" disk names, such as (hd0) and (hd1), but it does map these to real device names in the file /boot/grub/device.map. Update this to be correct for your new box, and rewrite grub to both your disks, using the grub command:
grub> root (hd0,0)
grub> setup (hd0)
grub> root (hd1,0)
grub> setup (hd1)
Then, check that /etc/fstab and /etc/mdadm/mdadm.conf don't contain any references to your raw disk names. Swap partitions are a frequent culprit, if you didn't put them in a RAID partition.
Reboot, and you should be going! Well, hopefully. Hope this helps.