Start with checking firewall:
# sudo iptables -L
or check it the "easy" way, disable firewall temporary:
# sudo service iptables stop
Then try to connect to webserver. If it works, then you know it's a firewall issue. You probably need help adding correct allow rule, just report back so we know it is the firewall.
If it doesn't help, post output of:
# sudo iptables -L
# ps aux |grep apache
Also describe the network - webserver (= "my own machine" ?) ip, LAN subnet, switches, routers, firewalls whatever you have.
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