Let's have a look at a few steps that can help resolve the issue. Try each step before moving on to the next one.

1. Please remove the battery and reinsert it after some time. When removing the battery, confirm that no dirt has entered the camera's contacts or battery compartment. Check the contact points and gently wipe off dirt with a soft, dry cloth before reinserting the battery.
2. Let's double-check if the camera battery is fully charged by using the supplied charger. If your camera doesn't have a removable battery, use the charging cable that came together with your product. If the battery is completely empty, it might take a while before it starts to charge, so take your time.
3. Meanwhile, if you have a spare charged battery, use it to test the camera. Speaking of other batteries, make sure you use original Sony batteries. Third-party manufacturers may not provide an adequate charge or qualitative contacts.
4. If you've done all the battery checks, investigate the power button or switch and ensure it's not dirty or stuck. Wipe off any dirt with a dry cloth and press the ON button/turn ON the switch several times.
5. If by any chance, you abruptly took your camera from a very cold environment to a warm one, moisture may have condensed on the switches and power circuits, preventing your camera from turning on. Don't turn ON the camera. Wipe off the moisture on the housing with a soft, dry cloth and let your camera acclimatize for 2-3 hours until the moisture has evaporated.