Comment by JoshuaZ

Uncomputable problems are not necessarily NP-hard. You can for example encode a version of the halting problem such that the instances are simply very long. For example, consider the language L defined by k is in L iff k=2^2^2^n for some n and nth Turing machine halts on the blank tape (some reasonable listing of Turing machines). In order to feed an NP-hard problem to an L-oracle, one needs to ridiculously expand the length of the problem far more than polynomial length so this certainly can't be done in polynomial time.