Recovery mode is not as simple as just keeping your finger on the power button.
Did you try it as documented on [Sony's official site](https://support.us.playstation.com/app/answers/detail/a_id/1488/~/safe-mode-on-ps3)?

I've copied the instructions below:

> 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.
> 
> Step 2:
> 
> 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). 
>
> Step 3:
> 
> 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)