Schematic for Lenovo ThinkPad W520 Wistron KENDO-3 WS Motherboard
The first component that is after the DC Connector its a fuse F14 that is rated for 15A and 24V Max.
If you don`t have voltage in both sides (like 19v Aprox.) change it with a compatible fuse that is rated the same like in the schematic.
If you wanna do a DIY job with wires start with tin wires so you won`t destroy the board just in case of a short.
Q28 is the second component after the fuse. If you got voltage on the fuse and still you can`t power up the notebook check the source,drain and gate on Q28.
If you got no voltage on gate on Q28 check Q31,Q32,Q36 and Q37.
If you got no voltage on gate on Q29 check Q30,Q33 and Q35 and resistor that is on the gate line.