  We report a new technique to select 1.6<z<4.6 dusty Lyman-alpha emitters
(LAEs), over a third of which are `blobs' (LABs) with emission extended on
scales of 30-100kpc. Combining data from the NASA Wide-field Infrared Survey
Explorer (WISE) mission with optical spectroscopy from the W.M. Keck telescope,
we present a color criteria that yields a 78% success rate in identifying rare,
dusty LAEs of which at least 37% are LABs. The objects have a surface density
of only ~0.1 per square degree, making them rare enough that they have been
largely missed in narrow surveys. We measured spectroscopic redshifts for 92 of
these WISE-selected, typically radio-quiet galaxies and find that the LAEs
(LABs) have a median redshift of 2.3 (2.5). The WISE photometry coupled with
data from Herschel reveals that these galaxies have extreme far-infrared
luminosities (L_IR>10^{13-14}L_sun) and warm colors, typically larger than
submillimeter-selected galaxies (SMGs) and dust-obscured galaxies (DOGs). These
traits are commonly associated with the dust being energized by intense AGN
activity. We hypothesize that the combination of spatially extended
Lyman-alpha, large amounts of warm IR-luminous dust, and rarity (implying a
short-lived phase) can be explained if the galaxies are undergoing strong
`feedback' transforming them from an extreme dusty starburst to a QSO.
