The first thing that I thought of when I read your post is how you determined that you NEED to upgrade these machines. Have you spent time watching the system performance monitor on each machine? Do you know what resources are being heavily used and what resources aren't? Microsnot Windows software comes with some absolutely awesome system monitoring software. Use it.
Once you have this information then you will be able to determine the answers to your question.
You may not need to completely replace your servers. You may find that your servers are page thrashing. In a case like that you could just increase your RAM. You may find that your hard disks are being heavily used. Maybe purchasing newer/faster disks will fix that problem.
So, researching the causes of your current problem will lead to the resolution.
=============
I hate seeing perfectly good equipment being replaced without first seeing if enhancing the existing equipment would do the job. It doesn't matter what you have in place if it will do the job. I would avoid purchasing new equipment just because the existing equipment is old, for instance.
Maybe you could take some of the retired desktop computers and use them as additional backup domain controllers. If money is going to be spent on equipment it may be better spent on replacing desktop computers. Then the old desktop computers can be put into service as network service providers, like domain controllers and DNS servers and stuff like that. A lot of network services can be spread out among many computers. Domain controllers fit this model. You can have a bunch of backup domain contollers, just as you can have a bunch of backup/slave DNS servers.
If you spend whatever money you have on things that people will see and use directly every day then your reputation among the user community will be enhanced. This will filter up through management and will get to your manager through word of mouth. The entire user community, including managers of other departments, will see you as a strong asset to the business because they can see how you have made their job easier. And everyone likes to see a new machine on their desk. Nobody cares about new equipment in the server room.
So, very often you can forget about buying new equipment to provide network services. Adding more old computers to the mix can be a better way to use exsiting resources. New equipment can go where more people in the business can see and directly benefit. By this I mean put the money into desktop computers and use old equipment for behind-the-scenes functions.