There is no easy solution to this problem. You will have to troubleshoot the logic board or have some one do it for you.
If you have access to the schematics and the proper tools, then you have to start at the beginning and check PP_BATT_VCC, PP_VCC_MAIN and PP5V0_USB. I would start by checking to see if those rails are shorted to ground. If one of these rails is shorted to ground, then you will need to identify what is causing the short. It could be a bad decoupling capacitor, conductive debris or defective IC that is directly supplied by those rails.
If they are not shorted, then you can connect, preferably, a known-good battery (or a current limited DC power supply with the appropriate connector adapter) to see what voltage you measure. If the voltage is low or lower than the battery voltage (which you measured before plugging it in ;>), then there could be a short circuit on secondary subsystem that is causing the battery or DCPS to be current-limited.
If you are measuring the proper voltage, then you move onto the PMIC and check the voltage rails it generates.