If it doesn't beep during boot, it isn't posting and your mobo is dead. At least, it is in a desktop, but it's a laptop, which means it could be a battery issue. Take the battery out and run it off the mains and try again. Also, try a new power supply (mains adapter) as this can cause the same symptoms. Make sure the adapter is compatible or you may cause more damage.
If it DOES beep (once) like normal, then you have a dead screen.
Dell warranty is pretty good and you usually get 3 years. Their products are also very good as self destructing just as the warranty runs out. I'd call them. If you are only a few weeks out, they may even repair it for free.