Fatigue has been one of the most debilitating and difficult to treat symptoms for me. It manifests physically, but I suspect now that my body would be mostly fine if my *mental* energy reserves were not so depleted by depression and anxiety. I find that if I stumble into some activity that is relatively mindless yet physically demanding, I can do it reasonably well. Running, sweeping, or any task, even if physically demanding, can be done if it requires little concentration.
So if that may be the case for you, you might try mindless physical activity to build your strength. Sedentary depression is different from the sort of depression where you're still functioning and doing school or work. It feels like if you just sleep a lot for a few days, weeks, even years, you'll finally stop feeling tired. Then (if you're like me) you try that and discover that you feel as worn out as ever because it wasn't your body that was exhausted; it was your mind. You try to return to more normal levels of activity, only you're as mentally drained as ever and now on top of that, your body is out of sync with your old physical routine and the physical weakness you feel is worse and more "real" than when it began.
tl;dr version: If depression tells you that you just need to rest for a while, and revert to being much more sedentary than your baseline level of activity, depression is probably lying to you. Some people do burn out in a physical sense but I don't believe that's ordinarily the case with depression.
Someone told me that the only treatment for this problem is to build back routine slowly, because doing what we do as a matter of routine is what makes it possible for us to complete relatively complex or demanding tasks. And because depression robs you of this benefit of routine, every single thing you do now requires more mental energy than when you were in the habit of doing it automatically. I believe that.
Oh, and I've known people whose depression-fatigue was ameliorated by Wellbutrin, too.