More background needed, really. (Score 2)

So what's the problem, then? We have a hard time finding parts to maintain the network. Our client says that he's willing to invest in hardware upgrades, but we should move to a Windows-like environment, however he doesn't want to pay for more than 4000 Windows licenses.

That sounds like two problems, not one.

You, as system supplier, have some sort of maintainance issue with the current set-up, the nature of which is not described in detail, unfortunately, but I can understand that identifying the particular application on /. may not be the best way of endearing yourself to the rest of your company and its current client, especially if, as it sounds, it's a custom implementation for that client. Meanwhile, the client is saying that if the setup is going to have to be be changed anyway, then they want to take the opportunity to upgrade the application and make it... what? Just prettier for the sake of it, or a more common PC-like look and feel so that there is less sniping from their customers about it being primitive and out-of-date? Or do they want added functionality as well? Are the existing central servers sacrosanct, or can that part of the app be adjusted, too?

I've got no concrete suggestions, but as this response indicates, I'd personally be inclined to sit down with the client and explore what they want and their reasons for it, and then, and only then, evaluate the approaches you collect.