You might try an external drive enclosure.
My old computer had a dead power supply and fried mb, so connecting the old and new would not help. I bought an external drive enclosure (about $35). After putting the old drive in the enclosure, it connects with the new computer via USB or Firewire. The old drive files are instantly available for transfer to the new drive, or for direct access on the external drive.
Both computers were XP. I doubt that this would work had the old drive been Windows 98 because of different file systems, but I havn't tried.