Hi Lisa,
I'd give a close look at Jeremiah Searcey, who was in Union, SC on the 1800 U.S. census (Ref: Year: 1800; Census Place: Union District, South Carolina; Series: M32; Roll: 50; Page: 223; Image: 438; Family History Library Film: 181425). He has sons under 10, so your William could be one of them.
There's a Jeremiah Searcy on the Roster of SC Patriots in the Rev. War: It says he died in Sep 1830. He had been wounded in the war & lost his left leg.
There's also a Jeremiah Searcy on the 1850 census that was born circa 1795. So I figured he was more than likely the son of Jeremiah from the 1800 census. I searched for him and located several family trees that showed him as the son of Jeremiah Searcy and Sarah Martin. Jeremiah Sr. shows as being born c 1758 in Granville, SC and dying 18 Sep 1830 in Washington, KY. He's shown as the son of John Searcy Jr. (1727-1791) and Annis Williams (1725-1790) (daughter of John Williams Sr. and Mary Womack). If you have access to ancestry, you can view the records here: http://person.ancestry.com/tree/19007019/person/19951521075/facts
It has a lot of information on Jeremiah Sr.'s military record, and also takes the family back to immigrant ancestors John Searcy Sr. (1694-1787) and his wife Phoebe Hargrave (1705-1783) from England.
