I use Debian 4.0, and I use both Yahoo e-mail and a Yahoo chat account.
For Yahoo e-mail, I use the graphical web browser "Iceweasel" (essentially Firefox), and go to http://mail.yahoo.com/
I've used it this way for years.
For my Yahoo chat account, I use the multi-format chat program "Gaim". Gaim can handle ICQ, AIM, and other chat accounts also. I use it for Yahoo and ICQ. Gaim has recently been renamed to "Pidgin", due to pressure from Aol. However, in the Debian 4.0 release, the program is still called Gaim.
Unfortunately, both Firefox and Gaim are graphical programs which require the X Window system. I don't know how old your computers are, but if they're connected by parallel cable instead of ethernet, I'm guessing they are OLD. As such, running the X Window system will be a strain--if it's possible at all. This depends on your specific hardware. Gaim doesn't require too much RAM, but Iceweasel is a RAM guzzler. I wouldn't attempt to run Iceweasel on a computer with less than 48megs of RAM.
What sort of graphics cards do you have? If you have graphics cards capable of at least 640x480 resolution with 8 bit color, then I'd at least give X a try. After doing a base Debian 4.0 install, log in as root and use the following to get X up and running:
apt-get install xorg menu aterm icewm icewm-lite icewm-themes
This will install:
xorg:The X Window system
menu: Debian's "universal" menu system that automatically adds/removes software packages from the menus
aterm:A very lightweight terminal for X, about 2megs less RAM usage than xterm.
icewm:A fast and lightweight window manager for your X interface
icewm-lite:An even lighter and faster version of icewm, but with less features
icewm-themes:A bunch of themes for IceWM. The "IceCrack2" theme is lightweight and looks nice.
For reference, I have an old 120mhz Toshiba Libretto 70CT with 32megs of RAM. With IceWM-lite and aterm running, RAM consumption is 12,708k. With fluxbox and aterm running, RAM consumption is 15,100k.
In other words, fluxbox uses up over 2megs more RAM than icewm-lite.