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I suspect you have a power problem. If you can run the camera (however briefly and as a test) with it attached to the AC Adapter/charger (if your charger is the kind that charges the batteries in the camera, not removed from the camera) and if the problems go away while you have it attached to the charger, that would confirm the problem as one of sufficient power provision (to charge and enable the flash circuitry, to take a picture - which involves a power demand surge - etc.)
Try removing the batteries, and leaving the camera on a (dry, non-humid, non-dusty) shelf for overnight. Then put the batteries back in and try the camera again.
Then try cleaning the terminals in the battery compartment, after removing the batteries, first by rubbing off with a fresh pencil eraser, then by wiping the terminals off with cotton swabs moistened in rubbing alcohol, then letting them dry off for 5+ minutes with the battery compartment door open, then try turning the camera On again.
You might possibly have a battery/batteries that are getting weak. Rechargeable batteries do get weaker with time, and eventually fail to deliver enough power to start up a device like a digital camera; they then need replacing. The replacement battery needs to be charged up for 6+ hours before its first use, owing to its having been on a shelf for a considerable time.
How old is the camera? exactly... if less than 1 year from original purchase date, then it is still within warranty, if that is useful to the case.
Has the camera been dropped or otherwise subjected to mechanical shock(s) in its lifetime?
Has the camera been operated in or subjected to, temperatures below 32 degrees F (freezing point) or above about 100 degrees F ?
Has it ever been subjected to a humidity higher than 85 % or gotten wet ?
Has the camera been operated in a gritty or sandy environment, such as a beach, a seaside, a construction site, or the like?