Customizing Knoppix is a ★■◆● and a half; you'd be better off using something like
Slax.
Though what you're asking for will require you to configure a few things:
1. You'll need to configure the bootloader (GRUB or LILO, the program that's in charge of loading the Linux kernel into memory) to boot straight to Linux. Shouldn't be too hard (if you use GRUB, it's 2 extra lines in grub.conf).
2. If you've got any sort of standard NIC, the tulip or 3com driver should be able to use it just fine. If you wind up having to compile the kernel yourself, you may just want to bake those drivers in rather than loading them dynamically.
3. Getting the static IP set up isn't hard, assuming you're going to set it once, when you burn the CD. You could also write a small script that prompted for it at startup and ran the appropriate ifconfig/route commands: "ifconfig eth0 <ip> netmask 255.255.255.0" and then "route add default gw <router IP> metric 1". Grabbing it from a USB key requires you to set up EHCI, UCHI, and OHCI (USB drivers) correctly and pray to God that your USB key doesn't do stupid stuff. Then you'd have to guess what device it got recognized as (it will be random) and then mount it and read your text file. In other words, it won't be easy to automate.
4. Bandwidth throughput testing endpoint? Like netstat? (run "man netstat" from a command line for info).
5. VNC server: you don't need a VNC server because you won't have a graphical user interface. Sorry Charlie, it'll just cause all sorts of problems. Instead, you can use SSH, which will allow you to access a command line from anywhere else. Say you get this thing up and running, and you want to access its command line from a Windows box. Grab
PuTTY (a free Windows SSH client), connect to the static IP of the machine running your LiveCD, and go to town.