you're the IT guy), then it sounds like some inventory management is in order. If you're providing support for a single company (i.e. If you're in a similar boat, then either tool I mentioned will work well enough. Usually I need to know things like 'what video card do I need to get to replace this one?' or 'what kind of power supply do I need to replace this one?' etc. I haven't had to physically crack a case to make a decision in quite a while.

like how many memory slots are available and free, etc. You can use a tool like Belarc Advisor on each machine to get basically the same information you can get from Windows, but with more detail. This tool will also report enough information about the system that you can tell, say, whether the video card is AGP or PCIe. Motherboard information is typically available from the BIOS and reported in the System Information utility in Windows as System Model. You can tell what kind of cards are installed, but not necessarily 'what else' you can install.

I'm pretty sure that it's not physically possible to tell what 'slots' are open in a machine without opening it up (other than memory).

Free real slots for desktop