Thanks, Ilian. You hit the nail on the head!
n[23]:= FullForm[wHexToDec["3FFBB67AE8584CAA"]]
Out[23]//FullForm= "+ 2^(0) + 2^(-1) + 2^(-3) + 2^(-4) + 2^(-5) + 2^(-7) +\
> 2^(-8) + 2^(-10) + 2^(-11) + 2^(-14) + 2^(-15) + 2^(-16) + 2^(-17) +\
> 2^(-19) + 2^(-21) + 2^(-22) + 2^(-23) + 2^(-25) + 2^(-30) + 2^(-32) +\
> 2^(-33) + 2^(-38) + 2^(-41) + 2^(-42) + 2^(-45) + 2^(-47) + 2^(-49) +\
> 2^(-51)"
If I apply ToExpression[ ] to it, I get what I wanted...
In[24]:= ToExpression[wHexToDec["3FFBB67AE8584CAA"]]
3900231685776981
Out[24]= ----------------
2251799813685248
Problem solved, thanks again!