If you just realized that an electrical device stops working when you turn it off, you shouldn't be running any servers at all. Basically, you should not even try to operate any sort of electrical device. You could seriously harm yourself.
Seriously: Do you have a TV? Can you watch TV when you turn it off?
The only way to have a server online 24 hours a day is running it on a machine which is running 24 hours a day. If you can't to this yourself, you will have to ask someone else to do it for you.
Here you can find the list of authorized TeamSpeak server hosters:
http://sales.tritoncia.com/hosters.php