If you want a system to try things out in APEX:
A) create an account on apex.oracle.com
B) install Oracle XE and APEX on your local machine (even if it is on your own machine)
As far as your Error 404:
It almost sounds like someone deleted your app while you weren't looking.
I really can't help but suggest you look at the log files.
Also, try using FireFox with the FireBug add in. That will tell you the exact URL that is being attempted.