The only hint I could find was this Sarah b in 1805. She might have been a sister. There were no other Purnells in this database who were born early enough to be his parents.
Family Data Collection - Individual Records Name: Sarah Seymour Purnell Parents: JohnPurnell , Sarah Seymour Minors Birth Place: Kent, Milford Neck, DE Birth Date: 25 Jul 1805 Marriage Date: 2 Jun 1825
In 1850 there was a Thomas and Elizabeth aged 59 and 52, farmers. They could have been his parents also. Name: Thomas Purnell Age: 59 Estimated birth year: abt 1791 Birth Place: Delaware Gender: Male Home in 1850 Murderkill Hundred, Kent, Delaware
In 1860 Jonathan was inUnited States Federal Census > Illinois > Sangamon > District 16