I'm not much of an expert on DNS but I was under the impression that those servers need an IP address to point to and one URL can't point to another, only to an IP address. So no static IP = nowhere for registered URLs to go.
There is a type of DNS record called CNAME allows for just this - redirecting one domain name to another. This would solve the OP's problem in the way that they would like, because the resolver would be the one looking up the asuscomm.com address, and not whatever is doing DNS at their workplace. I guess that GoDaddy is using a form of URL redirection instead.
Probably the best thing for the OP to do would be to talk to his ISP and lease a static IP, then point the GoDaddy domain to that... unless your Asus router supports another form of dynamic DNS hosting that is NOT blocked by their workplace.