Does the battery hold a charge ? Did you get a BSOD ? Did it give an error message when it shut down ? do you get any responce from the computer when you try to start it like post beeps or fan noise or hard drive noise . do you get any leds lite?

Here are some things to try First do a static discharge ,remove the battery unpug the power cord then hold the power button down for 60 seconds then plug it in and reinstall the battery and reboot . If this gives no Joy then try connecting to an external monitor . if this doesnt help try removing one dimm of memory at a time and booting to see if theres issue with the memory. If theres only one bar then find another stick of memory to see if that works . If one dimm of memory fails then the laptop will not boot. Try these and get back to use with your results so we can further diagnose your laptop