I'm new to road biking and just started this only to compete in triathlons.  I've had similar issues with different bikes I've used.  Here's what I've found so far (keeping in mind I'm a neophyte in the biking part of tri's).

First of all, move your grip around, don't keep your weight on the same part of your hands, move the point of contact around to keep the blood flowing to different parts. 

Next is seat placement.  I've found that if the saddle is too far back or forward than I have similar issues in my hands, arms and shoulders.

this is just what I've noticed in my very limited time on the saddle, hope it can help you a bit.

Hand numbness is very common in cycling because the handle bar tends to compress nerves in the hands when they remain in the same position for a long time.  The solution in to frequently change the position of your hands - sometimes only slightly.  Discovering different way to position you hands on the bars will eliminate the numbness.  If you're stuck in one position for a long time (in the drops fighting a headwind), shift your weight to one hand and let the other hand just hover on the bar and vice versa.  This will make sure that the blood flow continues and the nerves are relieved perdiodically.  Aero bars will also eliminate numbness in the hands but may not be appropriate for the kind of riding your doing.