My PS3 won't turn on. I attempt to start it up in Safe Mode but it wont stay "on" long enough to boot.
The unit emits two beeps and then turns off. What alternative methods can I use to boot to Safe Mode?
It doesn't sound like you're actually doing the correct procedure to get to Safe Mode, which is why you aren't getting there.
From Sony's website regarding the PS3. Emphasis is mine.
Activating Safe Mode
Step 1: Turn off the PlayStation 3 by holding the Power button on the front of the unit till the Power light is red.
Touch and hold the Power button (do not remove your finger from the button). You will hear the first beep, meaning the PlayStation 3 is powering on. Continue to hold the Power button and after about 5 seconds, you will hear a second beep, indicating the video reset. Continue to hold the Power button and after about another 5 seconds you will hear a third beep and the system will power off (Power light is red).
Touch and hold the Power button (again, do not remove your finger from the button). As in Step 2, you will hear the first beep, again for the PlayStation 3 to power on. Continue to hold the Power button and after about 5 seconds, you will hear a second beep for video reset. Continue to hold the Power button and after about another 5 seconds you will hear a quick double beep. At that point release the Power button. If you succeeded in activating Safe Mode, you will see a message on the screen saying, "Connect the controller using a USB cable and then press the PS button." Connect a USB cable to the controller and the PlayStation 3 and press the PS button to enter Safe Mode. You will now see the Safe Mode menu.
Step 4: We recommend performing the safe mode options in the following order until one of the options works for you. If one of the options work, do not continue onto the other options.
Restore Default Settings (item 2) Restore File System (item 3) Rebuild Database (item 4) Restore PS3 System (item 5)