This paper studies nonexistence of nontrivial nonnegative weak solutions for an inhomogeneous nonlocal weighted parabolic differential inequality in the whole space, involving p-Laplacian type quasilinear operator and the weight functions may be singular or degenerate at the origin. In the framework of test functions theory, modifying the nonlinear capacity method to derive precise a priori estimates and establish a new Fujita-type nonexistence theorem.