In dimension 4, we have the following: Simply-connectedness implies that $H_1(M)=0$. The condition that $M$ be a rational homology sphere implies that $H_2(M), H_3(M)$ are finitely generated torsion groups. It follows that $H^3(M) = Ext(H_2(M),\mathbb{Z})$, which is noncanonically isomorphic to $H_2(M)$ again (that's true for finitely generated torsion groups). But Poincare duality tells us that $H^3(M)=H_1(M) =0$, so $H_2(M)=0$. Similarly, we can obtain $H_3(M)=0$.
