I don't know exactly what the DPC3939 blocks in its various firewall modes, but the screen shot you supplied implies that only TCP ports 119, 123 are allowed for outbound connections in Maximum Security mode. Typically, the NTP service does sync operations using UDP; if the DPC3939 is blocking those UDP ports for outbound traffic, then it will be very difficult to sync with most Internet NTP services.
And FYI, doing an ICMP ping to a server in no way indicates whether any specific service is available on that server.
Do you have some specific reason for wanting to severely limit outbound protocols on such a wide scale? That is usually only something that is done in very restrictive and sensitive corporate and military networks.
EDIT: To illustrate what I mean about NTP normally using UDP instead of TCP, here is a snapshot I just took of my Linux server. You can see that ntpd (the NTP server) does not even listen on TCP, only on UDP port 123:
webhost:/ # netstat -a -n -p --inet --inet6
Active Internet connections (servers and established)
Proto Recv-Q Send-Q Local Address Foreign Address State PID/Program name
tcp 0 0 0.0.0.0:5901 0.0.0.0:* LISTEN 2193/xinetd
tcp 0 0 0.0.0.0:111 0.0.0.0:* LISTEN 2107/rpcbind
tcp 0 0 0.0.0.0:21 0.0.0.0:* LISTEN 2358/pure-ftpd (SER
tcp 0 0 0.0.0.0:23 0.0.0.0:* LISTEN 2193/xinetd
tcp 0 0 127.0.0.1:631 0.0.0.0:* LISTEN 2132/cupsd
tcp 0 0 0.0.0.0:25 0.0.0.0:* LISTEN 2405/master
tcp 0 0 0.0.0.0:3551 0.0.0.0:* LISTEN 1975/apcupsd
tcp 0 0 0.0.0.0:5801 0.0.0.0:* LISTEN 2193/xinetd
tcp 0 158 192.168.9.3:23 192.168.9.100:4432 ESTABLISHED 8185/in.telnetd: rw
tcp 0 249 192.168.9.3:42802 199.188.202.39:443 ESTABLISHED 8291/lynx
tcp 0 0 :::111 :::* LISTEN 2107/rpcbind
tcp 0 0 :::80 :::* LISTEN 1403/httpd2-prefork
tcp 0 0 :::21 :::* LISTEN 2358/pure-ftpd (SER
tcp 0 0 ::1:631 :::* LISTEN 2132/cupsd
tcp 0 0 :::25 :::* LISTEN 2405/master
tcp 0 0 :::443 :::* LISTEN 1403/httpd2-prefork
tcp 0 0 2601:5:1f00:571:e291:80 2601:5:1f00:571:e2:3514 ESTABLISHED 21956/httpd2-prefor
tcp 0 0 192.168.9.3:80 180.76.6.66:63097 TIME_WAIT -
udp 0 0 0.0.0.0:1007 0.0.0.0:* 2107/rpcbind
udp 0 0 0.0.0.0:111 0.0.0.0:* 2107/rpcbind
udp 0 0 0.0.0.0:631 0.0.0.0:* 2132/cupsd
udp 0 0 192.168.9.3:123 0.0.0.0:* 2280/ntpd
udp 0 0 127.0.0.2:123 0.0.0.0:* 2280/ntpd
udp 0 0 127.0.0.1:123 0.0.0.0:* 2280/ntpd
udp 0 0 0.0.0.0:123 0.0.0.0:* 2280/ntpd
udp 0 0 :::1007 :::* 2107/rpcbind
udp 0 0 :::111 :::* 2107/rpcbind
udp 0 0 2601:5:1f00:571:e29:123 :::* 2280/ntpd
udp 0 0 ::1:123 :::* 2280/ntpd
udp 0 0 fe80::e291:f5ff:fe9:123 :::* 2280/ntpd
udp 0 0 :::123 :::* 2280/ntpd
udp 0 0 :::177 :::* 1053/kdm