I experience that a lot. It's like I don't even exist...I hate it. For me, it can last for months, oftentimes out-living the depression that caused it. Sometimes I'll feel emotions, but they are as superficial as everything else. I'm normally very cold-sensitive (have really been suffering the last few days; the wind here is brutal!) but around this time last year I was in such a state and I just didn't care. I went outside without a coat. I was numb to the frigid environment; I was numb to everything.

From what I've read, it's a form of dissociation. If you don't feel real, then it is called depersonalization. If your surroundings are unreal, it's called derealization. Many people (including yours truly) deal with both. I hope that this helps you, and that you can get back to feeling (and hopefully something other than depression!) soon.