Whats the value for DNS when you leave blank DNS in static IP? When you set a static IP in iOS and you don't specify a in IP address for DNS, which IP does iOS use to resolve hostnames?
It doesn't have nor does it assign one.  However, it may have have host names/addresses cached so you may still be able to access sites you previously visited.  However, once that cache clears, you  will only be able to  browse by using raw IPs.