  In a previous paper \cite{Khlopov:2007ic}, we showed how the minimal walking
technicolor model (WTC) can provide a composite dark matter candidate, by
forming bound states between a -2 electrically charged techniparticle and a
$^4He^{++}$. We studied the properties of these \emph{techni-O-helium} $tOHe$
"atoms", which behave as warmer dark matter rather than cold. In this paper we
extend our work on several different aspects. We study the possibility of a
mixed scenario where both $tOHe$ and bound states between +2 and -2
electrically charged techniparticles coexist in the dark matter density. We
argue that these newly proposed bound states solely made of techniparticles,
although they behave as Weakly Interacting Massive Particles (WIMPs), due to
their large elastic cross section with nuclei, can only account for a small
percentage of the dark matter density. Therefore we conclude that within the
minimal WTC, composite dark matter should be mostly composed of $tOHe$.
Moreover in this paper, we put cosmological bounds in the masses of the
techniparticles, if they compose the dark matter density. Finally we propose
within this setup, a possible explanation of the discrepancy between the
DAMA/NaI and DAMA/LIBRA findings and the negative results of CDMS and other
direct dark matter searches that imply nuclear recoil measurement, which should
accompany ionization.
