External Power Switch for a Laptop

Something simple, but still maybe not as convenient as you'd like, you can set in the BIOS for the computer to boot when it detects power (available on many computers). This setting is for when a blackout shuts down your computer, and it's like a file server or something, so you want it to turn back on by itself as soon as it can.

My suggestion is that you enable this setting in the BIOS, plug your computer into a power strip, when you shut down, also turn off the power strip (I always do this anyway because it saves electricity, and my power strip hums slightly, which I can hear at night). Then, when you want to boot, just turn the power strip back on.

Note that hibernate mode does not require electricity like sleep mode does, so you'd have to use that instead of sleep mode if you are going to turn your power strip off.

If your computer usage tends to stay the same from day to day, you can time the computer to wake up instead. You essentially have to create a scheduled task that does nothing but makes the computer wake up to do.

You could also plug in an old mouse just for waking up the computer if you want (if your computer allows powering USB devices while asleep). Just follow these instructions but check the box instead of unchecking it at the end. Then to wake the computer, just click the mouse.

Both these solutions require that you put your computer to sleep, though.