Here is a list of points to follow in this case.
- check that all components are soldered (believe it or not, it happened to me once that I forgot to solder the 3V3 voltage regulator);
- check that all pins of the SD socket are soldered; since the kit comes with the SD card socket already soldered (by myself), any un-soldered pins is my fault (I apologize in advance if that happens; it did happen);
- with the multimeter, check all connections to the SD socket;
- make sure that the resistors in the voltage divider (4K7 and 10K, under the microcontroller) are correctly placed, as shown in photo 4 in the posting "Assembling Duino644".
Here is a tip on how to find out easily the polarity of a LED (especially useful for SMDs, either in circuit or not): with the multimeter's switch on the "check continuity" position (beeps), measure the "continuity" of the LED. The correct polarity will make the LED light up faintly.