After 10 years, maybe you need another direction. Not sure if I am any help, but...
I have an Eli Barnes, sometimes called Elijah, born probably about 1810, son of Adino S. Barnes and Alice (maiden name supposedly Norton, but pension app calls her Alice Punille).
The thing is, Eli and Elijah are not really common names in my Barnes family -- this Eli/Elijah is the only one I have connected. Father Adino descends from Thomas of Hartford and spelled the name Barns - no E. I descend from Eli's brother. They were mainly a Litchfield Co family - Adino and another of the sons lived and died in Canaan after HIS father married a Canaan woman. My ancestor (the third son) and the sister left the state.
Otherwise, this record was on ancestry.com:
Name: Eli Barnes
Birth Date: abt 1800
Age at Death: 30
Death Date: 18 Apr 1830
Death Place: Connecticut
Burial Place: Plymouth, Connecticut
FHL Film Number: 3358
If you want to check my info on Rootsweb, here is the link.http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&d...
Also check with Sherrie Haines: firstname.lastname@example.org
She is also from this family - maybe she has found more on Eli/Elijah.