Add in your uses the unit "WinNet". With the function "InternetGetConnectedState" return a value for internet state and type. See below:
function YourFunctionName : boolean;
var
origin : cardinal;
begin
result := InternetGetConnectedState(@origin,0);
//connections origins by origin value
//NO INTERNET CONNECTION = 0;
//INTERNET_CONNECTION_MODEM = 1;
//INTERNET_CONNECTION_LAN = 2;
//INTERNET_CONNECTION_PROXY = 4;
//INTERNET_CONNECTION_MODEM_BUSY = 8;
end;
update i newer Delphi versions add "wininet" as uses class.