Divide and Conquer.
It can get messy covering that much ground with limited resources. If they start throwing money at you, that could change things. What you want is to avoid becoming a one armed paper hanger. Enough metaphors. ;-)
The AS400 may take care of itself. Depends on how big it is, what they are doing with it, and whether they have dedicated staff for it. For starters, I would put that on hold as well as the Avaya. You can come back to it.
Another thing that will require particular attention is the active directory. Likely, they have an admin for that. Again, you can put that on hold and come back to it.
Backing up all the desktops might be over the top as well as too much unnecessary work. Like you said, a gazillion copies of the same thing over and over. What you want is to make the maintenance manageable as well as the backup. What we do is basically 3 different things. First, in as many cases as possible, we image the machines from a standard image held on a server. Second, we have user data on server shares. And, third, we tell people who want their own unique setup on their desktop that they are on their own. They can still save data to a server share, but we don't have the staff to help them with their unique thing.
Our Mac guy uses radmind to image the Macs in classrooms and labs. He has edited the NetInfo database for the Mac image to create a desktop link to the Samba shares on the server. Those links only connect if someone uses them. So, you don't immediately have hundreds of open connections just because all those Macs are running. He can modify an application and shoot out updates in the middle of the night.
Our PC guy used to use Ghost, but I think he moved away from that. He's been using grub with bootp and tftpboot off our Sun server. Images are there as well. He can interrupt the boot and request an update, or he can push them out at night. User and shared data is on a NAS.
For both of those, bringing up a new system just means entering it into our network database so that it will get an IP address and an image.
With that side of things in hand, all I have to worry about is the servers. The one thing I spent money on was an AIT5 tape library. I wanted to be able to keep full and incremental backups running back 6 weeks as well as archives and off site backups. This fills the bill. I then automated the backup process using Amanda. It typically leaves me with lots of free time to work on all the other things I need to deal with.
That's just one way of doing things. It works well for me, because I don't have to deal with all the desktop systems or the duplication of files across them. It works well for the desktop support staff, because they know I have their images and personal data covered.
Anyway, should be fun digging into all this and deciding where to go with it.
For links and reading, you can check:
http://www.linuxquestions.org/bookmarks/tags/backup