My laptop is a Toshiba Satellite L305D-S5938.

My laptop has recently started shutting down on it's own. I don't think it's because of overheating since I have a cooling pad. Anyway, this was still going on until one day after shutting it down, I didn't use it for atleast a day, and when I tried to turn it on the next day, only the charger and power LED were flashing, and the screen was off. I don't use a battery. I get power for my laptop directly from the charger. The problem is the hard drive LED. It usuallly flashes then starts blinking when the laptop is starting up, but this time it didn't. The fan is working fine though, and there are sounds when I turn it on. My main problem right now is the screen and the hard drive LED. Also, when I turn on my laptop, the wifi LED will start to blink. This has never happened before.

Also, if the hard drive or the motherboard is broken, will I still be able to recover my files inside?

Take out the battery,reinsert and reboot. Try to shut down the laptop by pressing the power button and see if it works.

I tried it, but it didn't work.

Try booting it without the battery itself.Is the hard drive running? Try presssing F8 or Del to get into alternative booting options at startup. If the HDD LED doesn't blink after that,then it is in someway related to the HDD.

first of all try to open bios at starting by pressing F8 Del F9 or F2 whatever for your laptop.

if still goes in dark, wait for a 5 minute .You have said fan is working and startup sound also .
OK after 5 minutes press Ctrl + Shift + Esc or Ctrl + Shift + Del to open Task manager.

if task manager opens do the following , i have the sam problem, :
when task manager opens in file menu > Run new task > type explorer , press enter.

if task manager doesnot open try to boot with other live cd like, ubuntu or fedora or mint.

if still doesn't
may be your screen is crashed.

If your data is important, you may want to consider having the drive removed. You can buy an external USB connector (about 25 bucks) and plug it into another pc to see if you can read/access the data.

I meant the usual engine running sound of my laptop, not the startup sound. Sorry for the confusion.

I've also tried the external USB connector, and nothing happened.

Try to connect an external monitor or screen first then turn-on your laptop again. Based on what you've said with these preliminary symptoms, there are many factors why your laptop's screen is just blank or just plain black. You said it was shutting down before, this might cause of (CPU Overheating) even though you're using a cooling pad; if your laptop is at its 3rd or 4th year of age and mostly you used it on your bed or any cotton based covering it might be possible that there is a clogged in-between the processor's fan housing and the fins of the heat sink. (Check if there is air going out of the ventilation side of your laptop) (if this is the case; then probably the Processor is most likely dead) Another reason would be an inadequate supply of power or current going inside the motherboard), try using another power adapter if you have a spare one. Try also reseating your laptop's RAM modules, Hard Disk, DVD-rom or try replacing it with a known good one. Try also observing those lights which are blinking especially the power LED and the Charging LED light and look at Toshiba's support site for KB articles. One questions my dear, did your laptop experienced any incident before like, liquid spillage, it fell down hard, etc...?

well, I did spill a tiny amount of liquid onto the right speaker, but it was a long time ago.