On the copy of Ubuntu Linux i got, it does not provide a "Graphic Safe Mode" it is version 11.10, newest version from the download website.
I'm sorry for giving you the wrong info. I've had next to no experience with Ubuntu 11. The safe graphics mode was an option on previous versions, so I assumed it would be available on 11.
I just booted an 11.10 live CD and the option wasn't there.
What you want to do at the boot options screen is press F6 for other options. Choose nomodeset. See here:
When you finish the Ubuntu installation you will be asked to reboot. If you get the black screen again after booting into your new installation, do this:
Reboot the computer and hold down the Shift key as the computer is starting to bring up the GRUB menu. The top line of the menu should be your new install. With that line highlighted press e to edit the entry. Use the arrow keys to move down to the next to last line. Change the text after quiet splash to nomodeset as I've done in the screenshot here:
then press CTRL-X to boot into Ubuntu
If you had to do that second step, you will want to set this as a permanent boot option to avoid having to change it at every reboot. To do that:
Open terminal. Type
gksudo gedit /etc/default/grub and press enter. This will open a text editor and you should see this on the screen:
Move down to GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"
Change "quiet splash" to "quiet splash nomodeset".
Click File > Save, then exit the text editor.
Back in terminal type
sudo update-grub and press enter.
That should do it. Good luck.
I tried Lubuntu on some of the older machines, it works on one, and another laptop has a faulty CD Drive.
If that laptop's BIOS supports booting to USB, you can install from a flash drive. You can use a program like Unetbootin to put the ISO on a flash drive. See here:
http://unetbootin.sourceforge.net/Since you've already got the Lubuntu ISO, you will want to follow the instructions here:
http://unetbootin.sourceforge.net/#other