Tomcat starts without errors but not listening on 8080

If the problem is that the port is not configured in iptables like Nash suggests, then you can configure it as follows:

vi  /etc/sysconfig/iptables

add the following line to the file:

-A RH-Firewall-1-INPUT -m state --state NEW -m tcp -p tcp --dport 8080 -j ACCEPT

save the file on exit and restart iptables:

service iptables restart

the answer of @alfasin is correct, but for CentOS 6 the comand line down not work

-A RH-Firewall-1-INPUT -m state --state NEW -m tcp -p tcp --dport 8080 -j ACCEPT

You need free chain one by one, this mode:

-I INPUT -m state --state NEW -m tcp -p tcp --dport 8080 -j ACCEPT
-I OUTPUT -m state --state NEW -m tcp -p tcp --dport 8080 -j ACCEPT
-I FORWARD -m state --state NEW -m tcp -p tcp --dport 8080 -j ACCEPT