I have some sympathy with the Polanyian position, which would probably 
rule
out what various non-human mammals do as "trade" or "market exchange."  But,
I think that we assume too much when we rule them out of certain levels of
awareness or consciousness.  Thus, it has been stated that they do not have
religion.  Oh really?  How does anybody know (aside from accepting tenets of
the Roman Catholic or other established religious entities that declare them 
lacking
in souls and hence not able to "have religion")?

Again, elephants come to mind.  I apologize that I do not have nice links or
definite sources, but I know that I have read that they not only recognize 
themselves
in the mirror, but clearly know who each other are in their established 
family groups.
It has been claimed that when a member of a group dies, the others behave in 
unusual
ways that some observers have interpreted as possibly representing some kind 
of
"mourning" activity on the part of the rest of the group, although this is 
itself anthropomorphosizing.
However, ruling out such an interpretation is itself also an assumption that 
cannot be proven.
I would note that the anthropological literature has long identified 
behavior relating to the
dead as evidence of religiosity in some form or other, e.g. corpses of 
Neandertals painted
red being viewed as such a sign.

In any case, if there is a deity, and elephants really know each other and 
mourn the loss
of one of their own when s/he dies, why would not such a deity provide 
comfort and
reveal itself to such beings at such a time?

Again, of course, the sorts of "exchanges" one sees in such elephant groups 
can be
viewed as non-market, much like socially determined relations within human 
family groups.

Barkley Rosser