  We report a Karl G. Jansky Very Large Array (JVLA) search for redshifted
CO(1-0) or CO(2-1) emission, and a Hubble Space Telescope Wide Field Camera~3
(HST-WFC3) search for rest-frame near-ultraviolet (NUV) stellar emission, from
seven HI-selected galaxies associated with high-metallicity ([M/H]~$\geq -1.3$)
damped Ly$\alpha$ absorbers (DLAs) at $z\approx 4$. The galaxies were earlier
identified by ALMA imaging of their [CII]~158$\mu$m emission. We also used the
JVLA to search for CO(2-1) emission from the field of a low-metallicity
([M/H]~$=-2.47$) DLA at $z\approx 4.8$. No statistically significant CO
emission is detected from any of the galaxies, yielding upper limits of
$M_{mol}<(7.4 - 17.9)\times 10^{10}\times (\alpha_{CO}/4.36) M_\odot$ on their
molecular gas mass. We detect rest-frame NUV emission from four of the seven
[CII]~158$\mu$m-emitting galaxies, the first detections of the stellar
continuum from HI-selected galaxies at $z\gtrsim 4$. The HST-WFC3 images yield
typical sizes of the stellar continua of $\approx 2-4$~kpc and inferred
dust-unobscured star-formation rates (SFRs) of $\approx 5.0-17.5 M_\odot$/yr,
consistent with, or slightly lower than, the total SFRs estimated from the
far-infrared (FIR) luminosity. We further stacked the CO(2-1) emission signals
of six [CII]~158$\mu$m-emitting galaxies in the image plane. Our non-detection
of CO(2-1) emission in the stacked image yields the limit $M_{mol}<4.1 \times
10^{10}\times (\alpha_{CO}/4.36) M_\odot$ on the average molecular gas mass of
the six galaxies. Our molecular gas mass estimates and NUV SFR estimates in
HI-selected galaxies at $z\approx 4$ are consistent with those of main-sequence
galaxies with similar [CII]~158$\mu$m and FIR luminosities at similar
redshifts. However, the NUV emission in the HI-selected galaxies appears more
extended than that in main-sequence galaxies at similar redshifts.
