You'll want to describe your network connection in a little more detail, and also whether you have a local ISP or if you're using AOL directly. And confirm if you're really using dial-up, and not broadband.
If you're on a telephone-line dial-up and not on a broadband connection, then you're on a telephone line and a modem of some sort, and it would appear that the dial-up or the telephone line or the modem or the modem at your ISP or at AOL modem is having problems, or services at AOL are not working.
If you're not using AOL as your ISP, then eliminate AOL tools and related, for the purposes of testing. See if you get errors with Firefox or related without having any AOL software involved. If you have an ISP separate and distinct from AOL, they could be having hardware or network issues.
If you're dialing into AOL directly (they still offer that?), then (if this is a laptop) then you may want to try a different access path; try connecting from a coffee shop or library.
If you're anywhere near the damage caused from Hurricane Sandy or connecting to servers in that area, then that storm has caused all sorts of communications problems.
And I'm guessing you're not really running OS X Server, a package that adds feature to OS X, and which is the usual subject of this forum. OS X Server is an extra-cost product that allows OS X systems to provide web services, to run a DNS server, to run mail services and other server-related tasks.