Okay. Let's do the following and focus on just gathering some information and not changing anything.
For now we will set aside any troubleshooting via the performance and resource monitors. They may come into play later if we find that something is bottlenecking your Asus setup and causing the connectivity to drop.
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The little icon in the bottom right corner will display a window when you hover the mouse cursor over the icon. When the window appears right click, select "Open Network and Sharing Center".
Then in the upper left corner click "Change Adapter Settings". We are not going to change anything so if you mis-click or otherwise end up on some screen just cancel and go back.
The resultant screen should show you what network connections have been set up on your computer. I would expect at least 2: one for your home network and one for your work network. Not usual to find a couple of stray connections from other network connections that have been set up. They may or may not have been disabled.
Select each connection in turn and click "View status of this connection" in the menu bar above. You need to do that when the connection is working and when the connection is not working (i.e., the red "X"). The main objective is to get you comfortable going in to look at the settings that may eventually need to be changed.
To the left of "View status of this connection" is "Change settings of this connection". Click and "Allow". That screen presents various parameters that can be set to establish a working network connection. There are even more settings deeper in. You can explore those if you wish but, again do not make any changes and just cancel out and go back if you feel something is amiss.
There is also a "Diagnose this connection" choice in menu bar. If one of the connections has a red "X" then you can select that connection and choose to have Windows diagnose it and possibly correct it. Since the home network connection is not what it should be as I understand your posting then probably no harm in proceeding with a diagonosis.
Hopefully there will be no requirements to make any BIOS changes. Also agree that if all the other computers on your network are working then no need to tinker with the router.
The focus is on ensuring that the Asus based computer is properly configured to communicate in the same manner as the other computers and devices on your home network. (Note: At some point you may need to look at one of those "normal/expected speed" computers to compare settings.)
That is enough for now. Just click around, observe, and see if you can get a sense of how it all fits together and works. Usually anyway.
Please note and post, as best you can, what you find. Thanks.
Side bar: Who manages and maintains your home network meaning the modem, the router, printer, cabling, configuration, security, etc.? Have you had that person take a look at your computer?