LAN Messenger is free (actually open source) and will do everything you need.
There is a Windows build of it (as well as builds for Mac and a few popular flavours of Linux) which runs just fine on Windows 7 (I use it every day), that supports plain text messaging between different computers on the same local network.
It has a user interface very similar to online chat clients, allowing user's to set their status (online, away, offline etc.) and for other users to see this status, and will show a popup in the task bar when new messages arrive.
A few additional features it supports:
- Broadcast message (You can send a normal message to all online users)
- Private chat rooms (chat between selected users)
- Public chat room (chat that can be joined by any online users)
- Direct file transfer (send files to other online users)
- Avatar image (users can set an image for themselves, both custom images and from a pre-made selection)
For the sake of disclosure: I am the packager of a portable version of LAN Messenger, but am in no way affiliated with LAN Messenger itself. I don't and can't earn anything from any download of LAN Messenger or any derivatives of it.