Mac App Store app can't be uninstalled, won't finish installing
Seems to me you should contact apple support.

I can think of several diagnostics here.


Is it apple ID specific?
Is your DNS servers having trouble or not local enough so apple knows where you are and which CDN node to use? Make sure you use the ones from your ISP.
Lastly, you may want to test with another user account, and make sure the app store functions correctly there.
If you can get away with it, does it work in Safe Mode? (holding down shift at boot)
When you run a traceroute, is the latency really high? What about speed?
What OS are you using? Snow Leopard, Lion or Mountain Lion. Mountain Lion probably has a much more integrated app store, and it might work better for you. (major surgery though.)