Network and DNS issues are not related to ownCloud as oC is just a webapplication served by your server. So moving this to the “Miscellaneous” category.
So you can use ownCloud for about 5 minutes or does it try to connect before it eventually fails?
Make sure the request pass through your router and passed to your ownCloud server. If that works, you must check your webserver settings. There is a wide range of errors and debugging requires some knowledge. Some tools that might help you:
nmap: can do port scans, you can use it on a computer outside your network to check the open ports
tcpdump: you can record all network activity on a network interface. You can for example run this on your server in order to see if any query reaches your server (even if your webserver is not correctly configured)
host/dig: check the domain name resolution