I don't know how to get a kernel dump from dmesg. Of course, when the no keyboard/no mouse situation occurs, I can't run dmesg or look at any logs or anything else. But I've looked in /var/log/syslog, var/log/messages, and /var/log/debug and haven't found anything around the time the lockup occurred that would give a hint as to what's going on.
From experience I can say that it seems totally random, not related to any particular program, not when the system is straining with a lot going on. To me it seems like some process has taken over the system and won't give space to operate the keyboard or mouse. But I can't check this out at all.
I'll be happy to troubleshoot if I'm told what to do.