http://tinyurl.com/ycvnqxd

if ping ya.ru <> 0 then showmessage('Connected');
Как то так.

Или же первая ссыль в гугле говорит нам, что:

function IsConnectedToInternet(lpdwFlags: LPDWORD): Boolean;
const
WininetDLL = 'wininet.dll';
var
hWininetDLL: THandle;
dwReserved: DWORD;
fn_InternetGetConnectedState: function(lpdwFlags: LPDWORD; dwReserved: DWORD): BOOL; stdcall;
begin
Result := False;
dwReserved := 0;
hWininetDLL := LoadLibrary(WininetDLL);
if hWininetDLL > 0 then
begin
@fn_InternetGetConnectedState := GetProcAddress(hWininetDLL,'Interne tGetConnectedState');
if Assigned(fn_InternetGetConnectedSta te) then
begin
Result := fn_InternetGetConnectedState(lpdwFl ags, dwReserved);
end;
FreeLibrary(hWininetDLL);
end else
raise Exception.Create('Unable to locate function InternetGetConnectedState in library ' + WininetDLL);
end;

procedure TForm1.Button1Click(Sender: TObject);
const
INTERNET_CONNECTION_MODEM = 1;
INTERNET_CONNECTION_LAN = 2;
INTERNET_CONNECTION_PROXY = 4;
INTERNET_CONNECTION_MODEM_BUSY = 8;
var
dwConnectionTypes: DWORD;
begin
dwConnectionTypes :=
INTERNET_CONNECTION_MODEM +
INTERNET_CONNECTION_LAN +
INTERNET_CONNECTION_PROXY;
if IsConnectedToInternet(@dwConnection Types) then
ShowMessage('Connected.')
else
ShowMessage('Not Connected.')
end;