If their's not a single LED lighting up or anything for even a split second I would personally investigate the power source to the laptop at first as it can be the cheapest to repair since it is a common issue with most laptops.
I have an Packard Bell laptop that is seven years old.
However, if it's seven years old it is probably using a motherboard without the solid-cap capacitors so it may be a distinct possibility that a capacitor has blown. Before taking it into the shop and spending $150 for them to look at it, it may be worth getting a small philips head screw driver and look under any easilly removable covers on the underside for any leaking, blown, or bulging capacitors.
They will look something like this