If the machine is manually shut off you cannot expect it to wake up via network communications.
If it is in sleep mode or Energy saver and is not waking up then you need to upgrade to the latest firmware. Do not do so if your current firmware starts with 071, in that case have a tech do it via "Altboot no data backup no clone" or you will have more issues than you do now. (This does wipe the device completely so every setting will be wiped out completely and it will be required for you to set it up manually)
Please be sure to select "Accept Solution" and or select the thumbs up icon to enter Kudos for posts that resolve your issues. Your feedback counts!