Is a "Stack up" the same thing as the system effectively "hung" - that is, no processes will run?

Does the system respond to a Ctrl-Alt-F2, that is, switching to command console 2? Is the system completely frozen?

Is there any way, either by switching to a console, or by examining after the fact, any log messages to get an idea what is going on?

The files in /var/log can give you some idea of what is happening, beginning with /var/log/dmesg to see messages during the booting process, /var/log/messages to see the messages that are recorded, /var/log/boot to see boot messages, and so on. Poke around there and get some ideas.
/var/log/syslog is there as well, so check out all the logs you see there, should be educational.

If you cannot get to the console, you may have to boot/reboot, then don't pause, look there right away.

dmesg usually only has the current session, but most logs have 3-4 versions, so you can look back to previous logs to see what has been going on.

In the worst case, add a S to the boot command line and boot Single User, then you can get to /var/log to examine it.