  We present a search for a standard model Higgs boson decaying to two $W$
bosons that decay to leptons using the full data set collected with the CDF II
detector in $\sqrt{s}=1.96$ TeV $p\bar{p}$ collisions at the Fermilab Tevatron,
corresponding to an integrated luminosity of 9.7 fb${}^{-1}$. We obtain no
evidence for production of a standard model Higgs boson with mass between 110
and 200 GeV/$c^2$, and place upper limits on the production cross section
within this range. We exclude standard model Higgs boson production at the 95%
confidence level in the mass range between 149 and 172 GeV/$c^2$, while
expecting to exclude, in the absence of signal, the range between 155 and 175
GeV/$c^2$. We also interpret the search in terms of standard model Higgs boson
production in the presence of a fourth generation of fermions and within the
context of a fermiophobic Higgs boson model. For the specific case of a
standard model-like Higgs boson in the presence of fourth-generation fermions,
we exclude at the 95% confidence level Higgs boson production in the mass range
between 124 and 200 GeV/$c^2$, while expecting to exclude, in the absence of
signal, the range between 124 and 221 GeV/$c^2$.
