The brain will not function well when sleep deprived, but it should not "shut down" completely. Research shows that lack of sleep causes mental, physical, and emotional health to suffer.
Therefore, you will have more trouble concentrating and doing simple tasks when sleep deprived. Having had insomnia myself, it is a terrible feeling not to sleep well.
I wonder why you are sleeping so badly. Have you really tried to improve how you sleep? I would suggest:
- Go to bed the same time every night, and rise the same time each morning. I know it sounds too structured, but it really can work.
- Take a bath, read, or do some other relaxing activity (one that you know helps you to relax) before you go to bed. This will help your mind to quiet down so that you can sleep.
- Try to exercise during the day to release your stress. Even simply walking outside for a few minutes can help.
- Sleep in a quiet, dark, cool room. Turn off the TV, as it can be distracting. Turn all clock displays away from your line of vision so you don't keep "looking at the clock".
If you have tried these simple things and you are still not sleeping, you should be evaluated by a health professional. Many health conditions can cause insomnia, so it is important to make sure that some kind of health problem is not complicating the picture. Good luck!