Is the system working well enough right now to connect to the network and transfer files? If so, it should be pretty easy to do without having to try to set up networking under DOS (which might be difficult, depends on if there are DOS drivers for the network controller on the laptop).
Put your Win98 CD into another computer that the laptop can see on the network. Then either share the CD drive on the network, or create a folder on the computer and share it, and copy the Win98 directory from the CD to that folder. On the laptop, open the shared folder or drive and copy the contents of the Win98 folder to a folder on the laptop in the root directory (c:\win98 is what I usually use).
Make a DOS/Windows boot disk. Reboot the laptop using the disk. Once you're at the command prompt, switch to the C drive, delete any directories you don't want, just be sure to leave the Win98 directory, and don't do a format of the disk. Assuming you have gotten ALL of your data files off the laptop already, you can just delete every folder but Win98, and all the files in the root directory (you may have some issues with read-only files; your boot disk should have attrib.exe on it so you can change the attributes). You could also copy all your data files to one folder and leave that along with the Win98 folder.
Once you're done with that, just go into the Win98 directory and run setup.exe.
If you need to format the partition, it'd be a bit more complicated, since you'd need to have a second partition on which to store the Win98 directory. You can use Partition Magic or a similar tool to do that (
http://www.igd.fhg.de/~aschaefe/fips/ is a free tool).
If you prefer to use a network boot disk, find the DOS drivers for your laptop's network card, and then follow
this, or
here seems to be a very simply process.