This definitely sounds like a problem with the router. Where (which hop) does the final destination show up with 0ms latency?

A 0 round trip time to the first hop isn't abnormal, but not showing any intermediate hops and showing 0 ms to the final destination sounds like a TTL Expired bug in the router. I would check for a bios update for the router. I'd also try the command-line TRACERT command to see if it behaves any different. There might be a problem with multiple outstanding requests in the router.

If you post a screenshot of what you're seeing (you can attach a .png image to a post), then we may be able to offer additional suggestions (based on the hop the final destination is responding).

- Pete