my first binary clock not working

You can simplify the display code a little more:

        // --- minutes ones

        digitalWrite( 1, (minute%10)  & 0b00000001); // 1's
        digitalWrite( 2, (minute%10)  & 0b00000010); // 2's
        digitalWrite( 3, (minute%10)  & 0b00000100); // 4's
        digitalWrite( 4, (minute%10)  & 0b00001000); // 8's

        // --- minutes tens

        digitalWrite( 5, (minute/10) & 0b00000001); // 1's
        digitalWrite( 6, (minute/10) & 0b00000010); // 2's
        digitalWrite( 7, (minute/10) & 0b00000100); // 4's


        // --- hours ones

        digitalWrite( 8, (hour%10) & 0b00000001); // 1's
        digitalWrite( 9, (hour%10) & 0b00000010)); // 2's
        digitalWrite(10, (hour%10) & 0b00000100); // 4's
        digitalWrite(11, (hour%10) & 0b00001000); // 8's

        // --- hours tens

        digitalWrite(12, (hour/10)   & 0b00000001); // 1's
        digitalWrite(13, (hour/10)   & 0b00000010); // 2's

Other suggestions to the code if you don't mind them at this stage of your project.
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