The new version of AOL Mail requires using ActiveX, which you can enable by changing your browser settings.
To do this, choose "Internet Options..." under "Tools" from your browser menu bar. Click on the "Security" tab and click on the "Custom Level..." button. Find "Run ActiveX controls and plugins" and "Script ActiveX controls marked safe for scripting", and set them to "Enable".
Alternatively, you can use the Basic version of AOL Mail here.