turns itself off after seconds and says corrupted files

My playstation 3 slim turns itself off within seconds after turning on. If you keep messing with it you can usually eventually get it to stay on. It says there are corrupted files. I have taken it apart and cleaned it. Added new thermal paste. I can hear the fan running. I have done a system update. I have put it into safe mode and done a file system repair. I’m not sure what my next step should be. I don’t want to delete all my saved files unless necessary, as I’m 75% on Skyrim. Do I need to try a new hard drive or power supply, maybe? Please help!