Im now using my laptop as a desktop unit, and it fits perfectly under my monitor stand - Apart from I have to pull it out every morning, open the lip/screen just to power it on

Is there a way I can power it on, without needing to open the lid? Or a remote/usb plug in power button?

Random i know, just trying to tidy up the office at home and its a bit of a bug bear for me...

Best way would be to source a docking station for it.

Dunc. The life you have is the only one you'll get; make the most of it.
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I used a USB docking station for mine for a good few years, a single USB connection interfaces screen, keyboard, mouse, speakers, network etc etc. The keyboard power button reliably started and stopped the laptop which was also set not to switch off when the screen was closed. BMW i3 Electric Car
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It really depends on the laptop and laptop capabilities.

I prefer to use mine as a second screen to my 34” ultra wide desktop monitor.

Anyway the capabilities vary wildly.

1. Some just can’t do it.
2. Others you can set the bios setting to wake on keyboard or mouse.
3. Others can use modern power settings in windows 10 which you can configure which ever way you want.
4. Other have literally a docking station support but likely won’t fit under your monitor as they tend to be bulky.
5. Modern laptops with thunderbolt can utilise a thunderbolt dock that both charges and controls your laptop.

My work one falls in that latter category. A 2020 Dell XPS 15. The thunderbolt dock has got an on off switch on it. Just a single thunderbolt cable to the laptop, and then from the dock a USBC cable to my desktop monitor. Then plug in my USB connections for desktop windows hello webcam, low latency mouse and keyboard and quality microphone all into the thunderbolt dock as well. So now with one button you can do it all.

But as the OP hasn’t mentioned what laptop this is about its impossible to give a conclusive response.

Both my kids now have monitors keyboards and mice plus other bits connected to a usb hub which they just plug and unplug as needed. Doesn’t solve the OP’s problem as my kids use the laptop screen as a second monitor, with home schooling as it is they run teams on the laptop and whatever else on the main screen. There is nothing that can't be fixed with a hammer😜😜
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What make/model of laptop is it and what monitor type are you connecting to. Some Macbook's require you to lift the lid to switch on and send a signal to the monitor to come on to. Ironically, some of the older Windows laptop that had a dedicated docking station rather than just a USB C style dock seem to be best at just having a single on/off switch that did everything 2011 TDV8 Vogue SE

Sorry gents (sexist assumption I know)

should of said, its this laptop: HP 6BL30EA#ABUBUN Laptop

Im the worlds biggest technophobe. The dock, or the 'switching on by mouse movement' sound best - if its do-able with my laptop?

That is relatively new so should be ok to wake on a USB Keyboard or mouse. But be warned it can be rather finicky with a number of different settings possibly cancelling each other out.

1. The BIOS needs to be supportive of this and have it enabled, you may even have to upgrade the BIOS.
2. Windows sleep settings and USB devices settings need to be aligned to do this.

It is only easy when you know it, and as a self confessed technophobe a road that will be met with frustration

This may be a decent starting point on configuring this;
https://h30434.www3.hp.com/t5/Notebook-Har...-p/6497676