This could be a lot of things. Start by removing the battery, if it is detachable, and try to power up with the ac adapter. The blue light on the end of the ac adapter should light up Blue if the ac adapter is good. If that doesn't work then put the battery back in and remove the ac adapter and try to boot. If neither of these boot attempts work then the problem is the mother board. You should contact Dell tech support to find out if the laptop is under warranty, usually 1 year unless there is a warranty extension.
If you get either a series of beeps or the Power, Battery and WIFI LEDs blink in a pattern then let us know so we can decode the error.