I'm really sorry that your parent is in the ICU, and good job on getting your work done through it all. But please don't use the fact that you can function right now to mean that others/OP could or should be able to function under less stress/personal issues. Your struggles don't diminish the importance of someone else's even if they are "less" than yours. Please also allow yourself some grace right now if you do happen to not meet your own standards.
Also, you seem to be under the impression that people should just "get over it" if they're struggling because so is everyone else. If everyone's struggling, then effectively, no one's struggling (in that no sympathy should be given). But that isn't helpful. Yeah, everyone's going through the pandemic, everyone's facing their own issues. But just because everyone is struggling doesn't mean that no one should get help/sympathy/understanding right now.
Another thing: you seem to be confused as to why people sometimes don't get there work done when they appear to be "perfectly capable" of doing so. Well, when you think about possible reasons why, what comes to mind? Is it that people just don't try hard enough, don't care enough, or are too busy drinking/smoking/partying/socializing? Sure, all of those reasons could be possible, but I think you might also want to consider the possibility that there could be different reasons, such as: mental health issues like depression or anxiety; ADHD (speaking from experience, when it's untreated it tends to have a demotivating effect where you want nothing more than to do your work but you just can't get yourself to do it, or it takes forever to start), or different internal issues like a fear of failure (yes, this can actually be demotivating: if you're afraid that even when trying as hard as you possibly can you'll still fail, why even try at all?). I think you might be tying OP's problems to personal failure because you yourself might be facing some of these issues yet you're still doing your work. Again, just because you're capable of it through your struggles, doesn't mean that we can't have sympathy for someone who's struggling to do it. Assigning blame and fault and guilt doesn't help anyone here.
So how do we get people to actually do their work? Well, the first thing to consider is why they're not doing it, and the above reasons are all possibilities (and there are likely many more reasons). Then we need to consider how to resolve the above issues. Sometimes it's more complex than just telling them to "just try harder". That kind of "encouragement" can convey to a person the message, "it's so easy to do better, why tf are you such a fuck up that you can't?" And perhaps that's the exact message that you want to get across, but it's not going to motivate them.
Especially when someone is depressed, hearing things that are often perceived as put-downs can be demotivating. They think of themselves as more and more inadequate/stupid/terrible at everything the more put-downs they receive, and it gets to a place where they might feel so low and so awful that they struggle to get up in the morning because every day they must be confronted with their own failures. For some, perhaps, failure is motivating, but for many people, especially depressed people, failure says "I am inadequate and I should just stop doing this while I'm ahead, it's no use and I'll never get better." No it's not logical, but why tf would mental health issues exist if everyone was perfectly logical? And I don't think we should be making people feel bad for not being logical or for having mental health issues. But I digress: to return to the question at hand, how do we resolve these issues in order to get people to do their work? Imo, for some, therapy is a good option. Therapy greatly helped me with my own depression and anxiety, and as a result my grades shot up (and then when I started treatment for my ADHD, I did even better). For others, it's possible that all you need is EMPATHY.
Whenever something is bothering me, like a bad grade or something shitty that someone said to me, etc., sometimes all I want is for someone I'm telling about my problems to go, "man, you're right, that does suck! Here's a hug, and I'm here to listen if you want to vent." They might actually think I need to get over it, but not once, not a single time in my life, has someone telling me to just get over something helped me. It made me feel like my emotions were invalid, and I just ended up feeling more terrible and more unmotivated. Maybe you think OP's emotions are invalid, but we're here to help him start working. I don't think a bootstraps argument is going to work here. Instead, I'd validate OP's emotions, and then ask them if they'd like some advice. If they say yes, then, careful to avoid telling them to "just try harder", consider utilizing the knowledge that there's usually an underlying reason for not finishing work to say something like "maybe it might be a good idea to talk to a therapist about this, just to see if it's helpful."
Responding with kindness, empathy, and helpful practical advice has always helped motivate me to get my shit done if I'm struggling. No amount of me asking myself "why don't I just do better or try harder?" has ever motivated me to do anything but hate myself for my inadequacies.
Sorry I just wrote an essay basically lol, but I have a lot to say about this kind of thing because of the way my ADHD affects my motivation/functioning. Hoping that any of what I said made at least some sense!