Ok since i have not seen 1 straight answer here i go:
1. how to permanently fix the solid / flashing red light
PROBLEM:Your PS3 has overheated.
FIX: There is not much you can do (anymore). You could open it up and check the solders and coolingpaste on the GPU and CPU... but normaly it's to late for that.
2. how to permanently fix the flashing green light
PROBLEM:This means your PS3 fails to load the XMB.
FIX: with the PS3 off, hold down the power button for 10 seconds until you hear three beeps. Press the PS button on the controller and the recovery menu will load. Use the recovery menu to unbrick your PS3 by installing a firmware update or preforming other actions".
3. how to permanently fix the 3 beep issue
PROBLEM: The filesystem is corrupt or the USB device in your PS3 is malfunctioning!
FIX: Remove the USB device and reinstall the FW
4. how to permanently fix blank screen of death / no display issue
PROBLEM: LOL... do i need to explain?
FIX: You could check if there is still a signal coming trough the cable by replacing it or try the RGB instead of HDMI...