If it's very new... USB 2 drive (?)-- it may not be compatible with ol '98. USB 2 did not exist then.
You could take the old drive
out of the case --and install it in the new PC-- then you could access those files directly... and much faster. You would not even have to mount the drive to the case-- just plug it into the
mobo and
PSU and set it on the bottom of the case, or a small empty cardboard box (being careful not to drop it or knock it off) untill you transfer everything you need.
Or you could mount it permanently/transfer your files/wipe & format the drive and use it for backups/music storage.