We present an elemental-abundance analysis, in the near-ultraviolet (NUV) spectral range, for the extremely metal-poor star BD+44 493, a 9th magnitude sub-giant with [Fe/H] = -3.8 and enhanced carbon, based on data acquired with the Space Telescope Imaging Spectrograph on the Hubble Space Telescope. This star is the brightest example of a class of objects that, unlike the great majority of carbon-enhanced metal-poor (CEMP) stars, does not exhibit over-abundances of heavy neutron-capture elements (CEMP-no). In this paper, we validate the abundance determinations for a number of species that were previously studied in the optical region, and obtain strong upper limits for beryllium and boron, as well as for neutron-capture elements from zirconium to platinum, many of which are not accessible from ground-based spectra. The boron upper limit we obtain for BD+44 493, logeps(B) < -0.70, the first such measurement for a CEMP star, is the lowest yet found for very and extremely metal-poor stars. In addition, we obtain even lower upper limits on the abundances of beryllium, logeps(Be) < -2.3, and lead, logeps(Pb) < -0.23 ([Pb/Fe] < +1.90), than those reported by previous analyses in the optical range. Taken together with the previously measured low abundance of lithium, the very low upper limits on Be and B suggest that BD+44 493 was formed at a very early time, and that it could well be a bona-fide second-generation star. Finally, the Pb upper limit strengthens the argument for non-s-process production of the heavy-element abundance patterns in CEMP-no stars.