Look to see if a wire from the power plug has got trapped and cut. usually under metal shielding plates.
See if the BIOS battery is in place and not loose across any conductors. Any other conductive debris like nuts and bolts. They could be deep under a board, but a mirror and torch might just enable you to see in a bit.
After that you're looking at power unit capacitors and diodes. A $3 meter is all you need for a lot of jobs. Here, they're selling Chinese multi-meters for $2.99cents. The measurements are the same as my Fluke 100 X the price. However, you can only get a rough idea without removing the components. But, a large diode-solid in both directions-would be a good possible.
Good luck.