After realising the root partition was too small for the programmes I want to use, I decided to enlarge the root partition and do a fresh install which seemed to go well. So I updated the system.

Unfortunately with the next boot the system keeps cycling through the bios check before the splash screen. So I plugged in the boot stick and away the machine went until it reached the login screen.

At the login screen the keyboard was unresponsive.

Should I reinstall Slackware stable or is there an easy fix?

Reading your rather incomplete report, I presume your first install, before resizing the root partition was Slackware -current. And if that worked, then you might have messed up the resizing - your root partition is corrupted, the second installation went wrong and the kernel didn't load properly (modules not available?). Thus, your keyboard is not working.

You haven't detailed your resizing procedure, so I can't figure out what/if went wrong.
There is a convenient tool (works well) that I'd suggest to use when resizing:
https://gparted.org/liveusb.php

I believe the easiest fix would be to start from scratch, delete and redefine your partitions and get a fresh Slackware installation. Any other fixing operations would be more complicated.

Well I did a fresh install and found two problems.

The first was that the root partition was the root parition had no boot flag. Which was easily fixed when Slackware 14.2 stable was installed, and booted, I opened Gparted and assigned the root partition a boot flag.

The second was that while the machine was updating it installed a new kernel and I had opted not to run lilo. So following boots didn't find the kernel. Which again was the simple fix of running lilo.

Glad you solved it on your own. Indeed, there were some simple fixes.
None of the issues you've found were related to the resizing, but some omissions during the setup & update.