Connectivity from machines on DHCP to machines with static IP addresses

We have our Comcast cable modem (which is a Cisco DPC3939B) set up so that some machines on our LAN have a static IP address, while other machines use DHCP (with dynamic IP addresses provided by the Cisco device).

For some reason, we don't have connectivity from the devices which use DHCP to the devices which have static IP addresses.  (Clients on DHCP-connected machines can't access servers on static-IP machines.)

Everything else works the way I expect:

- clients on all devices (both those with static IP addresses and those on DHCP) can connect to servers on the Internet;

- remote machines can connect to servers on our static IP addresses;

- clients on our machines with static IP addresses can access servers on our other machines with static IP addresses.

Could anyone suggest what we need to do in our configuration so that clients on our DHCP-connected machines can connect to servers on our static-IP machines?  (If it matters, we only need connections on a few specific ports.)

Thanks in advance for any help!