Hello, and welcome!
/var/log/Xorg.0.log may show errors with X, with the VESA driver, or with the display.
When the platform locks up, I wonder if the underlying OS is still functional ... except for the display. I assume attempting to switch virtual consoles with Ctrl-Alt-Function keys doesn't work, nor Ctrl-Alt-Backspace to terminate X. Can you ping the platform from another workstation on the network? If so, can you connect to the failed system with an
ssh(1) session? This last assumes you have
sshd(8) running on the workstation in question, of course.