I haven't seen somehing like this in a very long time, yet I'm hoping that it still exists. I would've coded it myself, but alas, I only know PHP, and know not of a way to do this with it.

It's a mailing list that functions relatively similar to a bulletin board: one member sends a message to, say, emailbb@example.com , which then forwards it on to everyone on the mailing list. Then, someone replies to that message, and it is again sent to emailbb@example.com , which then proceeds to forward it to everyone else.

Does anyone know where I can find something like this? ...does anyone even know what I'm talking about?

It's called a listserver and most mail servers have list capabilities, have you asked at your ISP?

Lyris and ListServe are about the best well known ones

Are there any free services to do this? Is there something similar to this that I could use as an alternative?

I'm asking because it's going to be put to use for a non-profit school website, in which I have no budget but hosting costs.

Did you ask your ISP or website/email host provider?
Do you have a control panel or something for your mail server where you can activate list capabilities?

a Google search ?

If you're a master in php, I've seen mailing scripts in which you can create a unique pop3 mailbox on your domain, and then custom write a cron-job php script that will connecty, retrieve, and parse incomming email according to the subject line.

It wouldn't be easy, but worth the effort.

chrishirst:
I did do a google search, but none of these are quite what I'm looking for. Most, if not all, of those seem to be third party applications that run off of their servers, whereas what I'm looking for is a script to actually install on the team's website and have run from there.
I've looked through the control panel, and there are no options for a list server, but rather just a standard mailing list, where it sends out something when I specify for it to.

mgraphic:
That actually looks like a relatively attractive option. It doesn't sound too overly difficult, and it'll give me a chance to brush up on my PHP skills.