Ken,

I've a hunch this could be:

Isaiah M. Castle

Residence Dallas City IL;
Enlisted on 8/18/1861 as a Private.
On 9/12/1861 he mustered into "F" Co. IL 50th Infantry
(date and method of discharge not given)

Sources used by Historical Data Systems, Inc.:
- Illinois: Roster of Officers and Enlisted Men.

Unfortunately, Illinois service records are not yet available on-line

You have any other info on him which could narrow down the search?