Is It Possible To Turn Off Your Computer In Your Home Via Internet Even Though You're In Office?

Yes,it is possible to turn off your computer via Internet but you need to have administrative rights over the network and your computer must be a part of domain of that computer through which you want to turn off the other.For example I have an experience of turning off a computer via another in LAN environment,the command is like this: shutdown -r -f -m "IP address" t0.

My son just told me that if you have remote access, then you can do this.

You could always ssh into the computer, then use "shutdown -PH now" to shut it down. That works no matter where you are, LAN or no LAN.

Yes you can but you must have an internet connection
first you need to do three things.
1.go-to notepad and type these without quotes
"c:windowssystem32shutdown -s -f -t 00" and save this anywhere in c drive and u must name it as shutdown.bat.
2.sign up for a pop3 gmail account.
3.go-to start in your pc and then to all programs->microsoft office->microsoft outlook
it will ask u the mail id and password give the email id and password that u have created then click finish or next .the next step is go-to tools in outlook then send/receive->send/receive settings->define send/receive groups now u must tick the "schedule an automatic send/receive every" and set the time to 1 minute then click apply and close it.
Then again go-to tools->rules and alerts then click new rule and set a blank rule as check messages when they arrive and click next .
Step1: Give the condition as "with specific words in the subject"
step2: Click the specific word and give it as "pc shutdown" and click add and click ok and next
           give the action as start an application and select the file that you saved in c drive        shutdown.bat and then click finish.
Now u must have the microsoft outlook running always.
How it will work?
You must send a email to the id that u have created and the important thing is the subject should be this pc shutdown and the outlook checks the mail for every minute and if it found this subject which is the specific word it automatically shutdowns the pc.