1. Screen fails to light up eh.... Like can you adjust the screen brightness, or is there no light what so ever, perhaps the back light has failed, idk, see if you can adjust, OR use a torch, or your camera flash as a troch and put it close at the laptop screen, can you see a faint image? If you can, the backlight has failed, if the backlight hasn't failed, and the actuall LCD isn't working, it could be that the screen is not receiving a signal from the motherboard or the LCD has died altogether.
2. Do you have a computer monitor at home? Or a TV with HDMI? If so, plug an external display into the laptop, and boot it up, and see if you can get the external monitor to work, you may have to press on of the function buttons on your laptop, or press it with the fn key too. - If this does work, then that means your Graphics Processor Chip is OK.
3. Also, those flashing lights, what is the manufacture e.g Toshiba - L50 D 1DZ - and go on to the manufacturer website and see if those flashing lights mean anything. e.g. 3 flashes form the battery light and num lock light could mean RAM failure, but that is a example. If you can, look on YouTube on how to remove RAM, very simple, a kid can do it, see if RAM is causing the problem, it is not too likely, however, I have seen some Laptop not even display an error message because of that. Just remember to touch something metal to ground yourself, before touching the RAM, and don;t cause static build up, basically, don't scratch your hair or rub your feet on the carpet, and only touch the RAM modules by the sides/edges. But if you're not comfortable, don't do it.
Also check if the harddisk is spinning= and look at the harddrive activity light (if your laptop has one) (unless you have a SSD) and you say the fan is spinning.
Sorry for the spelling mistakes and messed up sentence structures, I am VERY tired.
OH YEAH, tell us the Make and Model of your Laptop. And your OS if possible.
P.S Post this on a computer fourm such as Britec's or Tom's Hardware.
Feel free to reply.