back = 再 turn back on = 再开机

Both os these are different. Turn one's back on sb : Ignore someone or leave a person alone or refuse to help a person. But here TURN BACK ON means to TURN ON AGAIN. This person is asking if the computer which was turned off hasn't turned on yet. e.g. A. Has your computer turned back on yet ? B. No. It is taking too much time, There must be a problem with the OS.

Normally computers "turn on" and "turn off" right -- that's the basic phrasal verb. In this case, the speaker added "back" to show that the computer was on before. The computer was on. The power went out. The computer came BACK on. Another related example... It was hot, I took off my jacket. Then it got cold, so I put my jacket BACK on. It's really a mixture of a basic phrasal verb (turn on) plus the speaker/writer adding "back" to be more precise/ give deeper meaning. Another example... After the hurricane, the power came BACK on. (It was on before and now it's coming on AGAIN.) Compare: Mom to child: "Put your jacket on!" (means = put it on) Mom to child: "Put your jacket BACK on!" (means = jacket was on, kid took it off, mom wants it back on AGAIN)

Firstly "turned back on": When you want to use a computer, you usually turn it on first. Then when finished you turn it off. When you restart a computer it turns off and then back on so by asking "Has your computer turned back on yet?" you are asking if it has finished restarting. This could also be asked if the computer has had a problem where it has not been turning on and after trying to fix it. Generally speaking to "turn ___ back on" means to turn it on after it has been turned off (hence, it had been on previously). As for "turn one's back on": Yes it can mean "don't take any notice of sb", but more generally, it means to not help or stop being involved with someone or something. For example, you can say: "Don't turn your back on your responsibilities!" "Don't turn your back on your family!" And, of course, it could be used literally if one turns around to show their back.

If you turn on a machine, you start it, switch it on. 'Turn back on' = switch on again. It is said if something was recently switched off. "Why can't I get on the internet?" "We turned the wireless off." "Well, please turn it back on."