One place to start to see if TCP/IP is communicating with each other on both ends of the crossover cable is run nmap on both computers. If you don't have it, download it and install it via yum, and then run a portscan on each system, and see what ports you are finding open.
This will help narrow down if the static ip's are indeed functioning and if all the tcp packets are passing to each other and not being stopped by iptables. Now with this being RHEL, I know Red Hat is notorious for going all crazy on iptables, so if the portscan with nmap doesn't work on either, then check your iptables firewall rules to allow those specific ports be open and/or set both as as DMZ hosts.
Let me know what you find out.