This sounds like a blown capacitor, diode, or other similar component. There is a strong possibility that your hard drive is still working. Disassemble the computer using one of the many guides on this website and remove your hard drive . Put the hard drive in an external dock (you can buy them online for ~$20) and attach it to another computer to extract the data. Alternatively you can find the circuit board with the damaged component by looking for burn spots surrounding a missing or damaged component. Once you locate the damaged circuit board you can try replacing it. Keep in mind that if part of the power supply is damaged then it probably took the other components with it like the motherboard, processor, and even hard drive. Because of this possibility I highly recommend checking to see if the hard drive is working before you attempt a full system repair.