This sounds like a nice project, but I think $100 per system may be a bit optimistic if you don't want to go with used parts. $200 apiece is definitely doable, maybe even $150.
Also, how many systems are you looking at? Like 1-10, or 20-30, or 50-100? If you've got a large-volume order, you may be able to swing a deal for bulk parts from some retailers. Also, it may be possible to find, say, a store with five old P3 Celeron motherboards and CPUs, but not one that has 50 of them.
It sounds like what you need is:
CPU: Pentium 2/450 or higher
RAM: 128MB SDRAM or higher
HD: Um, any hard disk would be fine
VIDEO: as cheap as possible, probably integrated
SOUND: as cheap as possible, probably integrated
MODEM: some sort of dirt-cheap modem
LAN: not needed
CASE: any ATX case
PS: any 200W+ ATX power supply
OS: Win95/98 -- as cheaply as possible.
It's probably cheaper to try and find cases and power supplies locally, since shipping will kill you on these (they're big and heavy). You should be able to get both for $30 or so if you can find a local computer store that stocks cheap cases.
Newegg doesn't have any motherboards with built-in modems, unfortunately. The cheapest ones they have are about $10.
It looks like Win95 licenses are running about $15, and Win98 licenses are running about $25 on Pricewatch (the "$7" ones on there do NOT include licenses -- they're just copies of the CD). I'd want to lean towards Win98SE here for better stability and driver support, but if you're *really* trying to keep the price down, you could use Win95. I don't think Linux would be a great idea for these systems; you're looking at totally clueless users here, and as nice as GNOME may be, it's still pretty confusing if you've never used a computer before.
Ideally, you'd want a cheap MB/CPU combo that has onboard audio and video, OR one that has onboard audio and a source of dirt-cheap video cards (something like an old RADEON, TNT, or original GeForce -- going older than that will just give you driver nightmares). Flipping through Pricewatch, it looks like a few places offer a cheap Duron/Celeron with a cheap MB (mostly using the older VIA and SiS chipsets) with onboard video/audio for under $70. Probably your best bet, although I've heard of Fry's having $50 deals sometimes (though probably for boards without onboard video). I would tend towards a Duron config, as a) they're cheap, and b) it leaves upgrade room if needed later.
RAM prices, unfortunately, are quite high right now -- 128MB of cheap DDR266 is running about $35 on newegg, and maybe $20-25 on Pricewatch.
Cheap hard drives will be tough to find. I mean, the *cheapest* hard disk that Newegg carries is a 20GB 7200RPM WD drive for $50, and I'm not seeing much of *anything* under $30 unless you want used drives (which is usually a bad idea). Let's say we can find a supply of new, warranted drives for $40 a pop.
This would put the total at:
$30 (case and power supply)
$70 (MB, CPU, video, audio)
$20 (RAM)
$40 (HD)
$10 (modem)
$15 (Win95) or $25 (Win98)
For a grand total of $185 with Win95, or $200 even with Win98. This assumes you use identical, new parts for all the systems. If you're willing to buy used parts, and/or configure them with one-off components and not care about them all having the same config, you can do noticeably better than this.