Measuring voltage drops from the regulator output to the chip 5V pins is good if its got a power distribution tree rather than a solid power plane, and will often help you find the area of the board that's drawing excess current. If its a power plane you are FUBARed and voltage drops probably wont tell you much
Also, you don't always need to fully desolder ICs. Its often possible to desolder just the power pin, lifting it slightly for SOIC and TQFP, or cleaning the hole carefully for through hole, 'springing' the pin into the center of the hole and carefully heating the pin and pad alternately with flux to reflow any solder whiskers. Check with a low ohm meter if the pin has been isolated successfully. Cut power tracks if you have to to narrow it down - if done neatly, they can easily be bridged once the fault is found.