If you have a multimeter, Id check to make sure the laptop power supply is putting out power. If the power supply has power at the jack then remove the laptop battery and try to power it with wall power and no battery installed. If it still doesnt work then its either a damaged power jack or main board is dead. *Voltage output measured at power supply should be close to that of which its rated for such as a 19VDC power supply at 18.5VDC etc. If its only 6 volts output then its too low to charge and power it for example.
This laptop is a core 2 duo and isnt worth investing much money into it beyond a power supply replacement if the power supply is bad or battery of battery is bricking the laptops ability to boot. A main boards cost would likely be upwards of $50 if you do it yourself. A computer shop + parts if a main board you would be paying the cost of a cheap low end laptop new to fix this old one.
