To do a network install over NFS without a CD-ROM, you will need to use the Slackware boot disks. For this operation, you are going to need 3 disks.
The first, the boot disk:
Slackware Boot Disks
For the purposes of this install, you could get away with bare.i, but as you have a laptop, you might want to give bareacpi.i a shot, as that will have ACPI support for your laptop. ACPI support is not required for installation though, so it isn't much of an issue.
Then, you will need the root disks:
Slackware Root Disks
You'll need install.1 and install.2 to get the installer going, and to do a NFS install, you will need network.dsk.
Installation over NFS is much the same as with a CD-ROM, just point it to the NFS share, and off it goes like normal.
On the server side, you will need to setup an NFS share, and then inside of that share, extract the contents of the Slackware CD. Actually, you could probably mount the ISO as a loop back and make that the share (that way you don't even need to burn a CD), or even just share the CD-ROM drive itself. Just do whatever works best for you, as long as the client can get all the files on the CD, it doesn't matter how the server is really setup.