Probably a lot of money, but try removing the battery and plugging it in. Sometimes battery issues can keep a laptop from turning on.
Also, are you able to check that the laptop is recieving power at all with the power adapter plugged in? Maybe there is a "plugged in" light?
If there's no indication of the laptop getting power from the power supply, then that could be a good indication of a broken power jack (inside the laptop), which can be repaired without having to replace expensive parts usually.