  We search for the flavor-changing neutral-current decays B->K(*)nu nubar, and
the invisible decays J/psi->nu nubar and psi(2S)->nu nubar via B->K(*)J/psi and
B->K(*)psi(2S) respectively, using a data sample of 471 x10^6 BB pairs
collected by the BaBar experiment. We fully reconstruct the hadronic decay of
one of the B mesons in the Upsilon(4S)->BB decay, and search for the B->K(*)nu
nubar decay in the rest of the event. We observe no significant excess of
signal decays over background and report branching fraction upper limits of
BR(B+->K+nu nubar)<3.7 x10^-5, BR(B0->K0nu nubar)< 8.1 x10^-5, BR(B+->K*+nu
nubar)<11.6 x10^-5, BR(B0->K*0nu nubar)<9.3 x10^-5, and combined upper limits
of BR(B->Knu nubar)<3.2 x10^-5 and BR(B->K*nu nubar)<7.9 x10^-5, all at the 90%
confidence level. For the invisible quarkonium decays, we report branching
fraction upper limits of BR(J/psi->nu nubar)<3.9 x10^-3 and BR(psi(2S)->nu
nubar)<15.5 x10^-3 at the 90% confidence level. Using the improved kinematic
resolution achieved from hadronic reconstruction, we also provide partial
branching fraction limits for the B->K(*)nu nubar decays over the full
kinematic spectrum.
