Usually move /jiggle the mouse, or hit a key/space bar should wake it up.
If in hibernation or if those don't work to wake up from sleep mode- then sometimes there is a reset button near the power button ,or have to do a quick push on the power button to wake up.
If those don't work, then explore deeper in to the power settings on that computer - check screen saver time out, & power options.
These can explain better than I and may have videos or step by step how to do it-
If none of that works -
You might have to look up how to check settings in the bios , maybe in the power settings the mouse wake up/keyboard wake up is not set up...