rather simple open up cmd in windows
type the following and hit enter:
Do this with a device that it on the same network I believe all os models windows, linux, android, ios, osx have this feature built in ping will tell you exactly how to check this you could also just make a batch file to do this automatically in windows ...
If I am understanding you correctly this is very simple to do often things that will block your device is virus scanners or security tools.
Be sure that if you are accessing your device remotely that you forward both ports 80 and 81 to external port 80 on your router.
Hope this helps I am interested though to see what mmiscool cooks up not sure what he is thinking along the lines of doing but either way there is a ton of ways to skin this cat if I am understanding you correctly.