Your Win OS would help and system spec.
Could suggest a long list but none that could be as well covered as in the AOL HELP list.Just click on the tab and you will see most poss answers under Aol broadband.
Dont be to quick to say the modem is at fault.----
(I have said the same in the past,was wrong)
Use the modem tools in the taskbar to checkout your connections/adsl modem.
"while for the second LED to come on" Could be down to the install of the aol hardware or software or even your system software or hardware. My modenm lights at bootup varies. The third light is the important one.