Can Student version Mathematica run Wolframe | Alpha? Always got error message "Request denied by Wolfram|Alpha server(3004)"
Yes. The student version should work fine. What where you doing which produced the error? If you're still seeing these problem you may wish to contact Wolfram technical support (http://www.wolfram.com/support/contact/)
There are a couple of things which might be causing this problem.
Is Mathematica able to access the internet?
Do you see any other messages when this goes wrong?