I have a similar problem. I feel absolutely unproductive and worthless which leads to even less productivity.
Considering I have a great and encouraging supervisor just exacerbates my guilt and self doubt. Recently watched a video on Youtube called "7 Ways to Maximize Misery" and it really hit me how every single thing mentioned in it applied to me. I've been given a great opportunity, to better myself and reach my potential, yet I'm just wasting it away.
Discussing my project with others is not really an option as everybody else is doing really different things which leaves me feeling lonely and isolated. Don't really have friends or a social life to speak of. I eat and sleep excessively while feeling slow and lethargic.

I know how you feel Patchi. I'm in similar situation where all the people from my group have left and I'm the only one working long hours in the lab. To top it of, my group is not getting any new PhDs for next year's intake. It's going to a long and boring year.