Quick review: Got a message about updates need to be installed.  Installed the.  On the next reboot the system is extremely unstable--will only run for, perhaps a minute or two before a no keyboard or mouse response hang.
Was able to boot into text and used YAST to manually rollback the set of updates.  Rebooted, but the system still hangs within a minute or two.  It takes either powering off or
<ALT>-<SYSREQ> r....e...i...s...u...b     to shut the system down.
 
As I see it, I have three choices now.  (1) reinstall 15.3  or (2) upgrade to 15.4 (3) go back into current broken system
 
Recent addition to this system:
The current 15.3 system is on a "spinning" HDD.  I just bought a new SSD. to replace the HDD.
 
Today I tried installing 15.4.  The only thing the installer would allow me to do is to replace the 15.3 installation with 15.4.  I selected the new drive, but the installer wouldn't proceed with the installation. 
 
I can upgrade the current system, but, that leaves the system on the HDD.  So, I carefully unselected all the choices, and backed out of the installation without making any changes to the existing system (beyond putting the new drive in).
 
I think (am reasonably sure) that if I unplug the HDD, I will be able to install on the SSD.  
 
So, rollback didn't fix. Do you have suggestions other than: unplug the HDD and install 15.4 on the SSD?  (migrating my data will not be a major chore, if need be)
 
Thank you for all the help.
 
Mark