Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
If there is no battery power left, nothing will display.
If the battery pack is damaged, nothing will display.
If the battery pack is not installed correctly, nothing will display.
Even if the battery time left does not display instantly, you ought to see 'CALCULATING BATTERY INFO...' displayed, at least.
Is that not seen either? Then, does the camera turn On again when only on battery power?
If the camera turns On again, but nothing displays, make sure the DISPLAY/BATT INFO button is not dead, clogged with dirt, or otherwise non-functional. Try using it when power is On and the camera is running, and see if it works then.
How old is your Sony camera?