Turn on your TV and make sure that it is set to the proper HDMI input;
Turn on your PS3 by pressing the Power button;
Hold the Power button until you hear a second beep about 4/5 seconds.
Now, you should see on your screen the options allowing you to to set the video settings. Navigate to Settings > Display Settings and adjust the correct resolution for your TV screen.
If this doesn't work, start your PS3 in recovery mode by following the steps described in this article and then select Restore System Files to attempt to fix damaged system files without deleting your data.