For me, I'm generally have a positive/optimistic outlook on life so I rarely feel run down or depressed, so I personally cannot relate to such feelings, though I've known people who have been treated for clinical depressions. By nature, I'm a very curious person, cautiously adventurous, and try to turn as much of life into a game as possible - because then it makes life "fun".
If your issues are stemming from depression, definitely seek out help. If it's not necessarily clinical depressions, but you are overwhelmed with everything, then there can be steps to try to see if you can get things back under control (at least mentally to depressurize the stress you are feeling). As noted above, first you need to ensure you remain healthy. To both help with your health and provide some positive achievements - write down a short list of goals to do each day. Goals like - drink 6-8 glasses of water, eat a fruit/vegetable (bonus points for more), eat 2-3 good meals, do some exercise (walk around the block, walk up and down stairs 5-10 times, lap your house/apartment, 10-20 crunches, 20 jumping jacks - just a small amount of something). Try to set a sleep window and a waking window that will give you at least 7 hours of sleep. When it's time to go to sleep, stay down even if it's hard to fall asleep. When it's time to get up - just force yourself to roll out of bed - and that is goal one for the day - check!
Try to do this every day until you don't need to think about it - then you'll be in a habit. If you miss items on a goal, don't beat yourself up. That's where my outlook on life is like a game. If you have a goal to reach on a game and you don't make it, you play the game again because maybe the next game you'll make your goal (like those addictive games like Angry Birds, Candy Crush, Bejeweled) - each day is the start of a new game, slate clean, try to reach your goals and obtain that "high score". Once your "life game" goals become easy, then slowly increase the level of difficulty to the game.
For any immediate obligations you have, besides keeping up your own health - write down a list of everything on your plate. After making the list, take a break to do something else - anything - then come back to the list. If you think of anything else that needs to be done, add it at this time. Once the list is as complete as you can make it, now it's time to group and prioritize. What items on the list are "easy to do" (like need to do dishes or laundry, need to grocery shop) - depending on how soon these need to be accomplished, add one of those to a "daily" or "weekly" goal list. For anything else, determine which need to be done and which can be put off a week or a month. Once you have things organized - take your weekly or daily goal list and post it somewhere you always go - refrigerator door, bathroom mirror, etc. With it posted, throughout your day, you will have this subtle reminder of what you hope to accomplish this day.
Set your mind to do the easy task - then you have a win down. Then see how many others get done. Again, if you don't finish the list, the next day is a game reset - a new day to try to make the goal list again.
Eventually, you'll start to work out where your priorities are so you can better focus your energy on the targeted tasks and can give yourself permission to ignore the future tasks because they will eventually have their day on the goal list. Once you start knocking off the goals, your life will start to come back into control and you'll better be able to manage future issues that come up - in working those into your daily/weekly goal lists.
Lastly, take time once a week to review and revise your lists - could be after the events of the week, some tasks you thought were important that you had on the list and may not have completed turn out to be less important than you thought, maybe drop them to a lower priority, or let them ride another week. If the list has shrunk, add some of the future or lower priority items to the list to give them a go for a while.
And to make things more fun - if you are doing some tedious job - if you have a favorite movie/adventure - imagine you doing the task is being a part of that adventure. Like if folding laundry is a bore, imagine folding the laundry is the key to winning some race or defusing one of those movie bombs - the faster you complete the task, you just helped your hero in the movie. Once the last item is folded - hear the triumphant music that plays in the movie when crisis is over. That typically puts me in a better mood and makes the boring tasks a little more fun.
That or if you watch TV shows - turn doing dishes or laundry into a "beat the clock" game - see how many clothes you can fold or dishes to watch during the commercials. Then next commercial break see if you can get further. By the end of a show or two - not only will you have enjoyed your tv show, but you'll probably have completed those other tasks as well.
I hope you are able to take the advice posted by everyone to help figure out a strategy to get yourself energized and motivated again!