Schematics can be incorrect sometimes, especially with "Revision B", etc.

It is best to replace the capacitor with the same value, voltage, and type as the defective unit. In this case, a 10uF, 16V Electrolytic (low ESR type suggested).

 

Does it matter which way round they go?

 

Orientation matters with polarized capacitors (electrolytic/tantalum). The small disc capacitor you are using isn't polarized, but it is also around 1/1,000,000th the size that is required, compared to other photos.

The side of the cylinder type electrolytic has a stripe down the side of the negative/cathode connection. On the board in the pictures above, there is a "+" on the anode size, which would be the "non-striped" side. Other boards use a half-filled circle, for those, look at other caps on the same board to find out if the white half of the circle is positive or negative.