Assuming you're on Windows, you may be able to use Remote Desktop Connection (aka "RDP") whether or not someone's logged in. But a separate concern there would be whether your inventory software can handle multiple simultaneous logins (if it's something like Microsoft Access, odds are not good).
RDP is what I use to reach our "headless" servers all the time (headless = it doesn't have its own monitor/keyboard/mouse, but I can connect remotely and use it with mine). Unfortunately for you, I don't set those up so I don't know if the network guys here do anything special to enable this. It *might* just be as simple as making sure the "Remote Desktop Services" service is set to start automatically at startup.
In RDP you basically open a new login on the remote computer whenever you connect - so you could be logged in as yourself, while I'm using it separately, etc. This is why whether the inventory software handles simultaneous users is important. Wouldn't want my work to over-write yours.
That might be a nudge in the right direction. I'm not in your area and don't know anyone who is, but using the word "RDP" with a local network guy should get them understanding what you're after.