Ugh.
I did my best to alleviate the immediate issue by moving kids off of computers and that seemed to help a bit, but I still think there must be some sort of issue with my switch or something. I'm not entirely sure what the problem could be, but I knew that 128MB was pretty lean for the clients so after school I collected all the old PC133 SDRAM I had in stock and installed an extra stick in each client. This brings me to 256MB RAM in each machine which should be adequate.
I figured out how to check on the switch settings and all the ports are running at full duplex, but I've got a parent here who's pretty saavy with network issues so I might have him probe around a bit more.
One thing still left me puzzled yesterday, and that was the fact that some of the machines were not showing the screen correctly. Things were showing tracks around the screen and the resolution was different on different monitors. This despite the clients all being the same make and model. Very confusing.
It's taken me a couple of hours this afternoon, but I finally figured out the problem. I noticed that the problem was only happening on certain monitors, Dell M782 models to be exact. The Dell 781P's, which are actually a year older than the 782's, were working perfectly.
After wading through the ltsp handbook for a while and trying all kinds of settings in my lts.conf (/var/lib/tftpboot/ltsp/i386/lts.conf) I finally found the one setting that fixed all my problems:
XRANDR_DISABLE = True
[Default]
LDM_DIRECTX = True
XRANDR_DISABLE = True
X_RAMPERC = 80
X_MODE_0 = 1280x1024
LOCAL_APPS = True
LOCAL_APPS_MENU = True
LOCAL_APPS_MENU_ITEMS = firefox
SEARCH_DOMAIN = 192.168.0.1 || Change this for your own network
DNS_SERVER = 92.168.0.1 || Change this for your own network
RCFILE_01 = /etc/init.d/chmod-resolv.sh