My laptop screen won't turn on?

Lately my Acer Aspire 5750G has been playing up a bit. One day I turned it on after shutting it down as normal the previous day and it made all the typical 'start up' noises (from the laptop itself, not the speakers) but the screen remained as it was, completely blank. I turned it off and on again and it did exactly the same thing.

Each time I turned it on, the 'power' button lit up and so did the little light-bulb symbol below my keyboard but nothing else did (for those who don't know, the little 'hard drive in use' symbol is supposed to light up on start-up). Then finally after my fifth try, the 'hard drive in use' symbol finally lit up and my screen turned on and the laptop started as normal. I had my time on it and then I shut it down, only to be greeted by the same irritating problem the next time I started it up. I've shut down/started my computer four times since this problem began, and it took five, three, six and four times respectively to get it to start up as normal. Anyone know of a way to fix this?

P.S. My charger jack is also a little bit broken and for a while a couple of weeks back my laptop went through a period where half of the keys on the keyboard didn't work at random times, just in case they're to do with this problem.