This problem I have seen quite a bit and has another quick fix all thanks to a recovery mode that is on the PS3. The recovery mode lets you restore the PS3 to its true original settings so if there are any bugs with the system, they get removed. The PS3 turning on and nothing on the screen is the most common bug but there are others such as the PS3 can read the disc but goes blank when trying to play it. Right now down to getting the PS3 into recovery mode.

Put PS3 into recovery mode

With the PlayStation on standby turn the PS3 on but do not remove your finger from the power button. This will eventually turn off again but it will make a clicking noise and sound a little bit different from the normal shut down.
Then turn on the PS3 again and again, hold your finger down on the power button. Now this is the part where you must listen carefully. There will be a first beep when your turn the PS3 back on, then another beep. Finally there will be a double beep; this is the point where you remove your finger from the power button.
Now this has reset the PS3 and it will go into recovery mode. You may have to plug in the controller to the PS3 via the USB cable to use it.
Once the PS3 has loaded into recover mode you will be given a few options.
Restart (restarts Ps3)
Restore Default Settings (Restores PS3 settings. Warning this deletes profile data)
Restore File System (Restores PS3 firmware)
Rebuild Database (Resets PS3 database. Removes all pics, music and games directories. All data on hard drive is still kept.)
Restore PS3 System (All of the above and it deletes the hard drive data.)
System Update (Updates the PS3 firmware)
From this you can pick an option to restore. Usually it is best to pick Restore PS3 System this performs most options but again be warned that this will delete all your data.