List of PC's running Office.

[king1]

They were never tied to an MS account back then so there is nowhere you can look, other than on the suspect PCs.  I am not sure it will actually help though, I think back then it was just a limit on the total number of installs and how often...

TBH though I would suspect you will have trouble activating it anyway.  MS really want you to buy a new version and go out of their way to encourage it

How come MS can now say after all these years that I have used up my three installs if there isn't data on a server that they readily can access?

They do have that data on a server somewhere, that is how they know.  
But AFAIK they don't give end users a way to interrogate that data, and for privacy reasons it probably doesn't include anything meaningful that would allow you to identify the actual device.  I would guess they create a device profile made up of things like mobo models, serial numbers, n/w mac addresses etc 

Either that or they are just saying no to every activation.

From here it suggests online activation is a no go and you need to use country specific telephone activation
https://answers.microsoft.com/en-us/msof...4f073f20d6