Let's try and avoid any specific belief system, as that is a natural way go to when confronted by a question that seems impossible to answer. However, there are some interesting logical possibilities that we can bring up.
We've got five or six, depending on who you ask. Once you're dead, they would all be gone. No news there, but the consequences of their absence would impact our views of what's next. So, either it's lights out, or we still exist in some way. If we do continue to exist, we would be in a quandary. No senses means we couldn't see, hear, touch, smell or taste. We would not be able to "look down upon the Earth" and see what our families and the rest of the world were up to. That's a bummer, since I for one, would have loved to see things progress (or regress), or even just get a kick out of who showed up for my funeral.
What about thinking?
Since the electrical activity of the brain is required for thinking, that's gone—a no brainer, in a way. This logic seems reasonable, because if we could continue to think, we'd be at the mercy of our inherent IQ. If not, then folks with brain problems, like schizophrenia, or tumors, or other defects that affected their mental capacity, would be freed of all their physical handicaps and "think" in ways they never could while alive—all without that troublesome gray matter. That's actually a comforting thought. But "thinking" after death, if possible, would likely be an entirely different experience, one that we cannot imagine while alive. In fact, we'd have no word for it.
If there is an existence after death, then it would occur at an atomic or subatomic level, where the close interactions of bazillions of atoms and molecules were no longer required to keep a living body intact. Life and our devoted insistence on keeping our beloved DNA safe would no longer be important or relevant. Our new form of existence would likely be more like a quantum level conversation with the rest of the Universe. Don't you get the feeling that the mystery of the Universe should eventually be revealed? It's almost like we deserve it. We kind of expect that the limitations of our bodies stuck on this mote of a world would at some point fall away, allowing us to become in touch or rejoin the infinite expanse surrounding us.
Of course, it's just a feeling, I know. It would be so sad, if it weren't true.