sevenjen, I am not sure if I can help or not.
I have installed Puppy slacko 5.3.1 to my ASUS tower and ASUS laptop and all is working fine. Both are installed to my hard drive.
What are your 2 computer specs and are these frugal or full installs.
When attempting to update to Puppy slacko 5.3.3 or to Icy Slacko 126.96.36.199 I find that the boot discs I created run well in ram on my tower but have refused to oblige me and install fully when used on the laptop.
How are you attempting the upgrade. It matters depending if these previous installs are full or frugal installs.
Just so you know. I run various Puppy Linux's. MacPup 528v2, Puppy 520, Puppeee 4.4, Racy 5.2, LightHouse 5.0.1, all frugal installs. Some are on external flash drives, others on internal hardrive partition. I have never tried to upgrade my installs to the next version release. I just update the applications by hand. Like Browser, Flash, or Java, and sometimes make a personal .pet like Jitsi from a Debian .deb package.
I am mainly replying so you can elaborate a bit more on your hardware and explain explicitely on what you are trying to do I guess.
Above are install upgrade threads. I hope they help you.
The installations to ram seems to go along okay but invariably stops at the splash screen, but at different places. The dog barks sometimes with no icons present. The icons have loaded at times, but when attempting to run, say, Sea Monkey, things seize up.
Also, are you doing a md5sum check of downloaded Slack0 isos before burning on good cdr disks at slow speed.
I know you said it boots on the tower but not the laptop. Just checking to be sure. Hardware specs may help clear things up also. Maybe you need the xvesa option at live boot instead of the xorg option also. Just guessing here though. I don't run slack0 so I may not be off much help though.