Several individuals have done much research on the Shaddrick and allied families, and my e-mail exchange with two of them, Gloria Gore Jones and James Sheffer, is contained at the end of this section. We have managed to document much of this lineage through our interchange, and Gloria maintains a file on WorldConnect which has even more information.
So far, we have been unable to find the names of the parents of Linsfield and John Shaddrick. The only clues we have are the statements of the brothers in census documents that their parents were born in Tennessee, and of course, the last name of Shaddrick. Unfortunately, many people were illiterate in the mid 1800's and the Shaddricks were all farmers. So the census taker had to spell their names for them. We have spellings for Linsfield as Shadrick, Shaddrick, Shaderick, Shedrick, Shaddick, Shadic, and more, so it's no easy task to find them.
The two best candidates we have for ancestors are Nancy Shadrick, 1840 Illinois census, widowed or divorced, with two boys the right age, and Thomas Shaddrick, 1810 Kentucky census. We haven't found any record of Nancy past the 1840 census, and can't find Linsfield or John in the 1850 census (they are found consistently in later censuses, always in Johnson County, Illinois).
It's always frustrating not to find someone in a census, but in the 1850's and 1860's, the two censuses where families tend to disappear, much was going on, notably the gold rush and the civil war. Linsfield would have been about 18 and John 14 in 1850, and in those days it was common for 14 year olds to seek their fortunes alone or with an older brother. They may have gone to the mines in California or Colorado, maybe made some money, and returned to Illinois. Their mother may have remarried or died. Linsfield's future wife, Lydia Ann Gore, is found in 1850 in Johnson County, and both brothers married in the mid 1850's in Johnson County, so we know they mainly lived there. I just finished going through the 1850 census for Johnson County, Illinois, line-by-line, to make sure they weren't just missed or misspelled in the indexing process, and didn't find anyone remotely resembling the Shaddrick family.
The reason for looking so hard for Linsfield in the 1850 census is that it is very common for a widowed mother to be living with her son, and finding her would give a first name and other information.