To me, it sounds like the system update scrambled the video resolution, which is why your screen is going black. The system is probably still running fine, but the monitor can't work at whatever resolution the system is now set for.
Try pressing the CTL + ALT + F1 key combination. This will bring you to one of the multiple text-mode virtual terminals. If you can see some standard text asking for a login username, the system is running and the display works.
Log in as root. If that goes well, try running...I don't remember if its now called "video" or somesuch; I usually typed "drakex" (all without the double quotes, of course). This will start a text-mode video setup utility for XWindows. Choose a generic VESA driver regardless of what you've got. If your monitor can handle it, choose a comfortable screen resolution, say, for example, 1024x768.
You'll have to navigate with the keyboard arrow keys, the space bar, and the enter key. When done and the new settings are saved, try starting the X server by typing "startx" or, if the server is already running, pressing the CTL + ALT + BACKSPACE key combination to force a restart of the X server. If the system doesn't switch you back to the graphical screen, you can reach it with the CTL + ALT + F7 or CTL + ALT + F8 combinations.
You can also do a simple reboot to see if changing to a VESA driver fixes things. You reboot from the command line by typing "reboot" (without the double quotes) or the more verbose "shutdown -r now"
If you can get to a graphical screen with the VESA driver and log in, go to the PCLinux Control Center (Menu -> More Applications -> Configuration -> Configure Your Computer) and reset the video settings (under "Hardware -> Configure Graphics/Configure Video Card"). Change back to the driver based on your video card, set your resolution that your monitor can handle, and click on "Test" to see if everything works.
You should be able to take it from there.
These are educated guesses as you didn't say what type of display you've got.. Yes, I know you said a particular computer make and model. No, I don't feel like looking anything up right now. Besides, you might have something non-standard, so I'm don't want to steer you too