If you're intending on displaying this site to the world wide web you'll need to forward the ports along inside your router for starters, but i'm not sure what changes you'd need make on the actual setup for the WP install (i havn't done that myself - always used a webhost).
If you're using ports 8888 and 8889, then login to your router and forward those ports to whichever IP gets assigned to your IP (again just an example) 192.168.1.5, and see if you make any further progress... OR see below..
Temporarily whilst getting things working(in a manner of speaking), you may find it easier to assign your IP(what's provided via the router), DMZ.. to avoid the port forwarding, once you know everything works, turn it off, and work on the ports, it'll at least make dealing with the ports a seperate setup, and you'll be able to clearly see when ports are the underlying issue.
DMZ in simple terms means don't block or filter any ports/traffic(so it's excluded from the routers firewall etc...) for the given IP (so don't leave it turnt on - you have been warned)... ;)