What I would do is since you have another computer, just plug the new drive into your current system and copy all the installation files over to it. I usually make a directory called win98.cd and just copy everything from the X:\Win98\ folder. (X:=CD-ROM) Then plug the drive into your new motherboard, boot off the CD-ROM (or anything you can, for that matter), change to C:\Win98.cd and type "setup."
One hint - if you're having problems with Win98 complaining that you're trying to install an upgrade version, or upgrade with an install version, or just plain tired of typing in the serial number, download [url=www.mindspring.com/~steel_rat/setupx.dll]this file[/url] and copy it into your installation directory with all the .cab files. I modified this file (so you know where it came from) using the directions I found [url=kickme.to/winblowz98/]here[/url] and it works great! (If you don't trust me, you can modify your file yourself.) I use it with Windows 98 Second Edition, but it should work with all versions of Win98.