Windows Server can't ping outside network when switched to static IP

I can no longer ping outside our network when I switch our server to a static IP. The backstory:

The server runs Windows Server 2016 Essentials with dual Broadcom NetXtreme Gigabit NICs. It was previously configured with one NIC on DHCP (192.168.1.228), one on a static IP (192.168.1.251). We were having sporadic network performance issues, and when I reviewed the server's logs I noticed frequent errors saying:

A duplicate name has been detected on the TCP network. 

The issue appeared to be the fact that the NICs had different IP addresses but the same server name. I set up NIC teaming for the two NICs with Default VLAN membership. Running nbtstat -n showed we had one dynamic IP for the NIC team, and network performance seemed to have improved.

I then discovered that one of our CNC machines was not able to access the server via its mapped network drive, which was pointing to the old static IP (192.168.1.251) of one of the NICs from before it was teamed. The CNC machine is on a separate subnet:

>ipconfig /all

Windows IP Configuration

Host Name . . . . . . . . . . . . : PPC01_101
Primary Dns Suffix  . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No

Ethernet adapter LAN:

Connection-specific DNS Suffix  . :
Description . . . . . . . . . . . : Intel(R) Ethernet Connection I219-LM
Physical Address. . . . . . . . . : 20-46-A1-02-E1-7B
DHCP Enabled. . . . . . . . . . . : No
Autoconfiguration Enabled . . . . : Yes
Link-local IPv6 Address . . . . . : fe80::d178:76cf:1b17:58bc%13(Preferred)
IPv4 Address. . . . . . . . . . . : 192.168.100.101(Preferred)
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Default Gateway . . . . . . . . . : 192.168.100.200
DHCPv6 IAID . . . . . . . . . . . : 270550689
DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-20-A2-4A-B0-00-05-B7-E6-F6-6E

DNS Servers . . . . . . . . . . . : fec0:0:0:ffff::1%1
                                    fec0:0:0:ffff::2%1
                                    fec0:0:0:ffff::3%1
NetBIOS over Tcpip. . . . . . . . : Enabled

The original vendor set up our HP 2920-48g switch to allow the CNC machine only to communicate with 192.168.1.251, so I can't ping the server name from that machine. I figured I would resolve the problem by changing the server's NIC team to a static IP of 192.168.1.251. However, when I change from DHCP to the static IP I can no longer ping outside our network from the server.

I can ping outside the network when on DHCP, but can't access the server from the CNC machine:

>ipconfig /all

Ethernet adapter Server NIC Team:

   Connection-specific DNS Suffix  . :
   Description . . . . . . . . . . . : Microsoft Network Adapter Multiplexor Driver
   Physical Address. . . . . . . . . : 10-98-36-AE-12-93
   DHCP Enabled. . . . . . . . . . . : Yes
   Autoconfiguration Enabled . . . . : Yes
   Link-local IPv6 Address . . . . . : fe80::99cf:7507:898:412a%11(Preferred)
   IPv4 Address. . . . . . . . . . . : 192.168.1.228(Preferred)
   Subnet Mask . . . . . . . . . . . : 255.255.255.0
   Default Gateway . . . . . . . . . : 192.168.1.1
   DHCP Server . . . . . . . . . . . : 192.168.1.1
   DHCPv6 IAID . . . . . . . . . . . : 185636918
   DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-20-25-75-36-10-98-36-AE-12-93
   DNS Servers . . . . . . . . . . . : 66.155.216.122
                                       207.59.153.242
   NetBIOS over Tcpip. . . . . . . . : Enabled

I can't ping outside the network when I set a static IP:

>ipconfig /all

Ethernet adapter Server NIC Team:

   Connection-specific DNS Suffix  . :
   Description . . . . . . . . . . . : Microsoft Network Adapter Multiplexor Driver
   Physical Address. . . . . . . . . : 10-98-36-AE-12-93
   DHCP Enabled. . . . . . . . . . . : No
   Autoconfiguration Enabled . . . . : Yes
   Link-local IPv6 Address . . . . . : fe80::99cf:7507:898:412a%11(Preferred)
   IPv4 Address. . . . . . . . . . . : 192.168.1.251(Preferred)
   Subnet Mask . . . . . . . . . . . : 255.255.255.0
   Default Gateway . . . . . . . . . : 192.168.1.1
   DHCPv6 IAID . . . . . . . . . . . : 185636918
   DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-20-25-75-36-10-98-36-AE-12-93
   DNS Servers . . . . . . . . . . . : 66.155.216.122
                                       207.59.153.242
   NetBIOS over Tcpip. . . . . . . . : Enabled

I still get the same problem when I temporarily turn off Windows Firewall on the server.