Well 56K is slow, very slow combined with AOL.
This is an Internal Modem right? RJ-11 cable goes right into computer?
So you don't have a router.?
Have you tried disconnecting and then reconnecting, it could be a slow server that you got onto when you dialed up.
But Im willing to bet that you got some spyware/Viruses, But since you have 56K, I Reccomend you download these free programs on another computer and use a CD-r or USB flash drive to get the install file to your computer.
Download these
Stinger
Hijackthis
Run Stinger, delete whatever it finds, then run hijackthis and then save the log file, open the log file and copy/paste that into a reply for us to look at.