First of all, the newly acquired IT department is the best place to start to ask questions. One is what the mainstream systems used is, second is what the notebook series used is, and last is if there are any out of the ordinary systems.
Second, the newly acquired financial department is in charge of depreciating those assets, and should have a complete list, all of the models, and all other information.
Third, generation of a tool or a scanner on the network or a emailed tool to take inventory of the system would be the next step.
Last, I would also see what their plans were as far as workstation replacement, then build a plan around what you find. But it is not a matter of talking to the people who work with the systems, but rather, working with the FA's who see the systems and are depreciating them.