Sometimes when I'm feeling like this, I can focus on one, tiny task at a time, and even though it seems like it takes forever, I can actually accomplish something very simple--so long as it's just one, simple, little thing at a time. And sometimes that will jump-start my brain to where I forget that I was trying to do just one, little thing at a time, and I'll accomplish a lot more than I thought I could.
But other times, even tiny tasks are overwhelming. So for me, "give in" is like previous posters said and just let the exhaustion/dissociation/discord/despair sit there for a while. Or if it's anxiety, find a way to address it head-on.
Earlier today, I was feeling very anxious and couldn't sit still or focus on my work at all. I really needed to get work done, but I had to calm down somehow first. I got it in my head that maybe I could try tapping. I've read about it, and tried it a little before with mixed results, but mostly ignore the whole idea. But somehow it just came back to me today as a possibility. So I took 10 minutes, found a video on youtube for tapping to relieve anxiety, and went through the video. The tapping itself probably wasn't the key difference, but just having a simple physical activity that also focused my thoughts ("I'm anxious, I'm very very anxious, and I accept this feeling, and I choose to love myself anyway, etc etc"), and I felt better. I went back to work, and have been much better focused since (though still not at my peak...but at least productive).
Maybe you can rummage through your toolkit a little and find something that doesn't normally work, but might this time. All you need is just the tiniest bit of momentum, just the slightest ray of light, and follow it along to some kind of release so that you can get back to doing what you choose to be doing.
HTH