Trouble turning E6400 on

Hello, I've had this issue for 2 days.

When I try to turn on my laptop, the power indicator lights up, but the screen doesn't. After about 5 seconds, I can hear the fan turning on, but still no image on the screen. Then the laptop turns off, Caps and Scroll Lock indicators light up and the Num Loock one starts flashing. I tried it with and without power. I've had some issues with this in the past but I've always managed to turn it on, though before loading Windows it would show an error msg: Time-of-day clock stopped. And also, when I turn the laptop off, it turns off, but after about 4 seconds it turns on by itself. And I cannot put it in sleep at all. Do you think this is a problem I could fix on my own or do I need to send it to Dell? And also, I bought the laptop in USA, but now I'm back in the Czech Republic, Europe. Does the warranty apply to foreign countries as well? Thank you for your answer