Your router should have the option to discard ping from WAN side.
But the blinking lights on the modem and router should not be a problem. Both devices are constantly checking if the other is alive.
Since you did say that without the...
Earthlink leases lines from several vendors for dial up POP access.
UUNET, LEVEL3, and I forget the rest.
Some of these lines are 33.6 only. Call ELN and ask for a 56k POP.
One detail you mentioned that you get 24k connections. This...