My LAN was working fine until just the other day. One Red Hat 7.3 box and one Windows 2000 Professional box, with the Linux box acting as the gateway. The second NIC in the Linux machine is set to 192.168.0.1 and the Windows machine is set to 192.168.0.2. I downloaded and started running gShield to help me setup an iptables firewall. Like I said, everything was working beautifully until I tried

/etc/rc.d/init.d/network stop
/etc/rc.d/init.d/network start

Since I did that I can't ping the two computers in either direction. I've taken a look at ifconfig:
eth0 Link encap:Ethernet HWaddr 00:A0:CC:A2:ED:F4
inet addr:24.168.80.247 Bcast:255.255.255.255 Mask:255.255.248.0
UP BROADCAST NOTRAILERS RUNNING MULTICAST MTU:1500 Metric:1
RX packets:361735 errors:1 dropped:0 overruns:0 frame:2
TX packets:53796 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:100
RX bytes:86347386 (82.3 Mb) TX bytes:5418660 (5.1 Mb)
Interrupt:5 Base address:0x9000

eth1 Link encap:Ethernet HWaddr 00:A0:CC:A2:2A:6C
inet addr:192.168.0.1 Bcast:192.168.0.255 Mask:255.255.255.0
UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
RX packets:8 errors:0 dropped:0 overruns:0 frame:0
TX packets:100 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:100
RX bytes:480 (480.0 b) TX bytes:4200 (4.1 Kb)
Interrupt:10 Base address:0xb000

lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
UP LOOPBACK RUNNING MTU:16436 Metric:1
RX packets:160 errors:0 dropped:0 overruns:0 frame:0
TX packets:160 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:14332 (13.9 Kb) TX bytes:14332 (13.9 Kb)

and route:

Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
192.168.0.0 0.0.0.0 255.255.255.0 U 0 0 0 eth1
24.167.80.0 0.0.0.0 255.255.248.0 U 0 0 0 eth0
127.0.0.0 0.0.0.0 255.0.0.0 U 0 0 0 lo
0.0.0.0 24.168.80.1 0.0.0.0 UG 0 0 0 eth0

Can someone please help me get my network running again?

If you cannot ping a machine, that means that you are either not on the same network and / or that there is no path (gateway) to machines on other networks.

Since you did not change anything on the Windows box, and since you cannot ping the Linux machine from the Windows box, your Linux machine is either not on the same network or the new software is blocking the pings. Your ifconfig data certainly verifies that you are still on the 192.168.0.0 network, so it has to be the firewall software.