Without knowing the context, to my mind "dead awhile" means for an extended period of time. Rigor mortis has probably set in.
For example, police break into an apartment at the request of a relative who has been phoning the resident without any answer. Police find the resident's body and do some preliminary checking - is his skin cold? Are his limbs stiff? Their immediate conclusion (before a medical examiner gives an expert opinion) would be that the resident "has been dead a while." If the person had died very recently, the comments regarding the body would reflect such. "He's still warm, he wasn't killed that long ago."
Student or Learner