When the author refers to "men whose abilities have been made for a time useless by their passions or pleasures, and who having lost one part of life in idleness, are tempted to throw away the remainder in despair," he means:
C. Men who waste their opportunities then grow mopey
Samuel Johnson is describing men who have wasted their abilities due to the pursuit of their passions and pleasures. The author is saying that men who do not put to practice their abilities end up wasting opportunities. However, these men later realize what they have lost and therefore end up being depressed*. This feeling is reflected when the author says that they "are tempted to throw away the remainder in despair." A remainder refers to what is left of something, in other words, they want to throw away the rest of their life and abilities in sadness.
*Mopey means depressed.