I noticed no one has replied to this thread, so here goes my first post. If your separate box with the server installed is a Windows machine, I'd suggest looking into wake-on-lan (WOL). I'm not certain, but I"m not sure Kodi natively has a way to wake the server machine.
I have WOL working on my machine at home and find it useful to wake my server when it sleeps while I'm at home or remotely with my android phone. WOL can be a bit tricky to set up, and you'll need to "port forward" on your router and/or modem.
Once WOL is set up you can, maybe, use a program called autohotkey to wake the computer with a push of a button or an action like "Watch TV"? I have not done this, but in principle, I think something can be done in that regard with some effort.
If that seems overwhelming, I've had good success going to the website below to wake my computer at depicus dot com:
https://www.depicus.com/wake-on-lan/woli
Alternately, I've used MPTvScheduler app on my Android phone, or you could try aMPdroid to wake and send the computer to sleep.
I hope this helps
EDIT, just did a quick search on KODI and there's an addon that does this when you start KODI or run the addon
http://kodi.wiki/view/Add-on:Advanced_Wake_On_Lan
