Press the "Menu" button on your camera. Does the LCD screen display the menu?
If not, your camera likely needs service.
It is possible to display the display for regular shooting. Repeatedly pressing the "Info" button will cause the display to cycle through several choices of what sorts of info you want it to display... but one of the choices is to remain off. However the LCD should always turn on when you press the Menu button as long as the camera is powered on (even if the display was otherwise disabled).
If you suspect a problem with the memory card, just eject the card and power up the camera. The camera can turn on even without a card (there's a menu choice that lets you choose whether the camera will let you use it ... vs. display the "No Card" error message. The camera wont be able to store any images, but it would still let you use it.)