You need to provide a bit more information. Does the computer have a RAID controller? Is it hardware or software based? Is it simple mirroring, or something like RAID 5?
On a single disk or mirrored disk configuration, you can just take the harddrive out and put it into a different computer to access the files.
If it's a more complex setup, you'll need to keep the array intact. Since the system is still booting, you can probably access the files through any normal boot environment. My preference is an Ubuntu Live CD. It's a bit tricky, but you can access NTFS partitions and then transfer data over the network. Alternately, you could move the drives and their RAID controller into another machine all together, but that's a slightly riskier proposition.