What your going to need is a bootable utility that can read NTSF disks and perform simple operations on files. Go to http://www.ubcd4win.com/
and make an ultimate boot CD. I believe you can do this in win98, but I'm not entirely sure. It is a very interesting utility that boots up and creates a pre-installed environment for you to work in. There may be other utilities that do the same thing.
Alternatively, if you boot from the windows XP CD you can go into a recovery console that lets you do a number of things. You might see if that works for copying files. Other things you might try if you get desperate. . . install a dual boot XP setup on your win98 computer. That would be able to read the new hard drive and you could copy the files into your win98 partition.