Why doesn't mail work with Att Yahoo servers?

Question

Ever since Bellsouth went to using Yahoo to handle their email it hasn't worked regularly. Now that my system is so old they are incapable of helping. They do not have any tech support for Apple products nor do they seem to care. The conversation all ways ends up that they say something is wrong with the mail program or the computer. Since i had it checked out I know that is BS.
I know there are a number of people using older Mac Mail programs with one of the At&T companies that someone must have found a solution, or not? There are pages of Mac owners complaining on the ATT site but no solutions.
Looking for someone that has succeeded in dealing with ATT and what is it?
It may be that the solution is using a different email program than Mac Mail or forwarding from a different email supplier. Any suggestions?

Answer 1

     Thanks to all whom replyed to my query. I have spent more time with ATT and I hired a local computer guy to help. Using you alls info and my high priced friend the email works most of the day. I have found a couple things... some say the servers are IMAP and some say they are POP. What I have had to do is have both set ups available to me to use to get and send mail. Right now the POP is working best.
     ATT will tell you either, depending on the fool you talk to. The last guy said only POP will work. The guy befoe said they were IMAP. They also like to send people to their 3rd party tech people. Unfortunately they don't know anything about macs and they won't tell you that until after you pay them. What the final say from ATT is that they only guarantee that you can get you mail via web-mail and will do little to nothing to help you othet than what is correographed on their computer screen. If that doesn't help thay basicly say tuff luck. My suggestion to all is find someone else other than ATT OR IT'S SUBS.
     Currently 2 of my three bellsouth.net emails address work a couple days at a time. One only works for 15 minutes. To get it to work you can open the Connection Doctor and run it usually once and the email will begin working again. You can access it (OS 10.8.4) by clicking on the little "triangle with exclaimation point" that comes up next to you email box name. I leave open all day to make it easier to access. It also makes the G5 work at the same time. Nor because they are connected but because the problem is with Yahoo-ATT.
     Current POP settings are:
                                    inbound.att.net     port 110 with SSL and password authentication
                                    outbound.att.net   port 465 with SSL and password authentication on two of the emails
     On one of the emails I have a GoDaddy web account that uses:
                                       pop.secureserver.net  default port selection with SSL and password authentication
for the out going mail server which works for the bellsouth email. Seems like it shouldn't but it does.
I also keep the IMAP settings as noted by "goodmanrc" as sometimes it works.
                   Incoming Mail Server
                      Host Name       pop.att.yahoo.com
                      Use SSL          ON
                      Authentication  Password
                      Port                995
                   Outgoing Mail Server
                      Host Name      smtp.att.yahoo.com
                      Use SSL         OFF
                      Authentication  Password
                      Port               25
The settings as noted by Andrew99 use to work before I got Uverse. Now they no longer work. At least not this week.
Thanks again to all.