There are two issues here:
1) First you need to check if your laptop has "Wake on LAN". If so, then enable it and make sure it is working locally.
2) After that, you will probably need to configure your router to allow the internet connection to be passed through. This may help - I've not tried it myself, but it does seem to be possible.
MSDN - How do I do wake on lan over internet?[
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