If you are trying to access JIRA from an external (global) IP address, instead of your local host, you might not have port forwarding setup on your router to access it outside of your local area.
To access it locally from any computer on your network
192.168.0.XXX:PORT where XXX is the local IP to that machine (eg http://192.168.0.101:8080) - This would be the first thing to check out to make sure you can access it from other computers on your network. To find the local ip of the machine you need to do an ipconfig (eg windows start -> run -> ipconfig -- look @ IP Address there). If you can't access it locally from another machine on the network, you might want to check the firewall settings on the computer you are running JIRA on to make sure it's allowed.
To access it globally, you'll need your real external IP (whatsmyip.net can give this to you - eg http://126.96.36.199:8080 --- random IP address i just typed FYI) If you can't access it that way, then you need to setup port forwarding on your router. You need to forward all port request (in this case 8080 for JIRA) to your local IP address. Linksys routers have a "Forwarding" area that's pretty explanitory. You enter the local IP address you want it to go to, the port number ranger (in this case both would be 8080), UDP/TCP/Both (use 'Both' if you aren't sure)
Each router is different. But it sounds like your porblem is port forwarding.