Don’t worry about your PC, the order should be executed at the server ! You can power it down when you sleep as soon as you have set your orders (at least with my broker, they told it to me, but it seems logical that for every broker, the various orders are executed at their server, not in your PC).
This being said, I don’t like automatic trailing stops, they are too mechanical, and they can lead to your trade being cut just on an temporary oscillation. They ignore previous highs and lows, Bollinger bands, etc.
I like using stochastics on a 60 minutes chart to exit a trade : usually it is quite reliable to signal a trend reversal, but this needs that you are not in bed at this time !
Another way to set your stop while you are sleeping is to use the Bollinger bands (on the winning side of the trade if possible), on a 5 minutes chart, or, if you are lucky enough to catch it, on a 15 or a 60 minutes chart, which is even better.
And also, if you can, before going to sleep, you can close half of your trade (meaning for example taking gain on 20 k if you have a 40 k trade), when you have : floating gain > 2 x (stop - trade). This covers any loss you might have on the second half if it comes back to your stop. Moreover, after taking this half of your gain, you can see whether you can reasonnably move your stop closer to your trade, or even protect your trade by setting the stop on the winning side of it, should it be only 1 pip above or under (depending whether you’re in a long or a short trade) from the trade ; Bollinger bands are a good indicator to set your new stop at this moment. This way, you are sure not to loose money when you sleep. At the worst you will have one half of your gain before going to bed + 1 pip. But be sure that your broker don’t allow slippage from the value of the stop at the closing of trades, otherwise you might encurr loses anyway.
P.S. : You say that your PC has to be running for your stop to remain in place ? This seems very strange ! Perhaps you should give a call to your broker to ask them how it works. Logically, the orders should be stored and executed from their server.