What should I do if a group project member is not contributing anything but is also depressed?

I have been in your shoes in a similar situation when I was in undergrad. Our group member was also going through some hard times and did not contribute much to any of the project reports that were supposed to be written by all of us.

What we did was notify the professor but in a way that showed we were concerned for the student. I think it makes a big difference how the professor is notified, since you definitely don’t want to put the group member who claims to be going through a hard time in a though spot (it is good to give the person the benefit of the doubt). What happened in our case was that our professor has scheduled a meeting with all of us (in your case would be a zoom meeting, I suppose) and we discussed all together what happened so far and what must happen for the group member to successfully complete the class. That worked for the person in my group, although he felt really embarrassed by this situation, he actually contributed more to the project and kind of put himself back together- not only in our project but in all of his other classes.

Additionally to this, I have contacted the person and offered to be there for him if he needed someone to talk to. At the time we were not friends and maybe this looked a bit awkward, but in the end we became really good friends and he actually became a great student for the rest of the undergrad.

So, in short, I know you must be frustrated, as well as your group members, but realize that you have to bury this frustration deep and try to address the problem while being helpful. You guys are still undergrad and have a long way to go ahead of you. You don’t want to discourage your fellow because of a small thing like a group project.

And believe me, you could help change his life by being supportive and understanding in this period.

Practically, you have no option but to share and complete his part of the work among the remaining parts of the group - the deadline is in five days, so not much can be done. The question is whether you decide to declare him as a full participant, as it is common practice in coursework (e.g. the "All members have contributed equally" statement in the cover, or an email to the module leader). I am inclined to give the benefit of the doubt for this assignment and suggest you included him as a full member, but take action for the next one. Contact the module leader, explain the potential situation, insist on not wanting the grade or workload to be affected and ask for his advice. I agree with the spirit of @Eylul, and hopefully it will go down that way, but if things go wrong you should ensure your work will not suffer and that you have followed the proper channels.

Also, be prepared to report the student to the student services if they show the same behaviour in the new assignment. This is not so much a moral but a practical issue. A mentally distressed person that does not fulfil student duties, is out of contact with staff and students, and does not reply to emails, is always a cause of worry for mental health officers.

If your doubts or your aversion towards doing someone else's work are stronger than the above, you should say on the cover that X did not contribute and in addition email the module leader and student services to see if any mitigating circumstances, like an extension or some adjustment in grading (unlikely), can be applied. If you have serious worries about the student's mental state (withdrawn for a very long time, suicidal etc) you should consider contacting student services now.