How to use Timer to exit LoopA,then run LoopB?

Projects Programming
7 
    quitTime = millis () + 10000;

Adding unsigned longs is not a good idea in robust code.

    do {
        // Do stuff
    } while (millis () - startTime < diddleTime);

is guaranteed to work. Though I suspect that a do/while is NOT the construct you want to use. While probably is. Look up the differences.