You need to change one of the boot parameters: nomodeset. Boot off the LiveUSB again and when you see the small human logo at the bottom:
Press and hold the spacebar. This will start the different configuration screen. Select your language and you will see a menu in the middle of the screen, and a set of Function key options down the bottom. Select the F6 option, then select nomodeset and press enter (and asterisk appears next to selection options)
Next press esc to close the window and select the "try Ubuntu" option from the menu. It looks like you might need to install some device driver modules after you've installed ubuntu, or make the nomodeset option permanent in the worst case. Ask another question here when you know what sort of graphics card you have. You can find out what the graphics system once you have the "try Ubuntu" option up and running. Open a terminal window with CtrlAltt and type
lshw -C display
and paste the output into your next question.