I get hungry, I get irritated. I get a 'don't care' attitude towards things. As the deprivation get's more severe, planning and thinking become harder. Some 'awake dreams' are a possibility , especially if I'm not doing anything physical. This leads to doubting my senses and my short-term memory and thus I begin to double-check everything. Concentration begins to severly suffer. Cramps and stomach-ache are quite possible as is headache. My eyes begin to twitch, as if I'm hyperactive instead of dead tired.
As more time passes, actual hallucinations are more than possible, incapability of focusing on anything with any degree, my eyes mostly just stare forward without focusing on anything and I operate on peripheral vision alone, short-term memories are unreliable and unlikely to be imprinted on my long-term memory - to just stand still without doing anything is enough for me to instantly fall asleep. While standing. With my eyes open.
That's the worst I've ever had and that was in a week-long military excersice designed to show us and our superiors our limits and how we behave under stress and deal with the lack of sleep. We slept around 9-10 hours total during those seven days while under strenuous physical activity every day and every night.
EDIT: But continuing to work is quite possible. In fact, on a medical excersise we had 50h of simulated wartime activity at a field hospital we set up fot the excercise. After around 45 hours we had an amazing period of having no patients. We went to sleep as fast as we could. Here's the fun thing: I never remember waking up. My memory is I went to sleep and next lucid moment is when I'm pushing an IV needle to a fake vein on my patients arm. I was later told we slep for only 15 minutes and that patient I remember was the third one I was working on after we woke up. So I treated, apparently correctly, two patients without remembering anything. And no-one noticing anything strange about my behaviour during that time, not even the bloody doctors/military officers we had overseeing and teaching us. It's a weird feeling I tell you, doing something complicated correctly without having a simgle memory of doing it.