Accessing the net means handing off your request to different servers. Usually do a tracert and it will show what part of your Hops are not getting through. It is quite a common error message.
Usually just waiting awhile clears up the congestion or in certain cases it is one of the connections to that server that is down for one reason or another.
Can you access the AOL mail server from another device? From a home computer? A work computer? If you use different isp's and say you can access on home and work computers then you know it is a Verizon server access problem, if another device on Verizon does the same it will confirm it.
If you cannot access AOL from home and work computers then you know the problem is on their end. Or their backbone provider. Level 3 or Cognant Net, AT&T etc.