The problem with their being no available parish, Legal or Transportation records is that there may be no further specific details on John. If court records had survived they might have given residence, accomplices etc. Ordinary people just didn't leave much of a paper trail..
There are about four entries for the surname Parnell in King's County on the Tithe Applotment records - all in Ettagh civil parish, which might be worth considering as possible relations to your Parnells. The Tithe records didn't include everyone, only certain types of agricultural land were eligible. Ettagh civil parish is located a little to the south of Drumcullen - just Seirkieran in between. Griffith's Valuation had far better coverage and would be more likely to show your Parnells exact location. There are only three Parnell entries for King's County on Griffith's all as Immediate Lessors - middlemen, or owners, but none as occupiers.
Parsonstown is the old name for Birr - originally the town was named Birr, then changed to Parsonstown and later back to Birr.
I had a quick look in Freeman's Journal for 17th July 1834 and the few days after but it's difficult going - the print quality/scan is not good. The King's County Chronicle newspaper covered this area, but as far as I can tell only started publishing in about 1845.
I see the single Parnell household in Pollduff, which is in Roscomroe civil parish. On the 1911 there are three young daughters and a son, so there may be descendants still in the area, although not all with the surname Parnell. The free IrishGenealogy website has images of marriage records up to 1941 and deaths up to 1966, so might help trace this family forward. I had a quick look through the records - looks like one of the girls, Julia died age 19 in 1915, another daughter Margaret died single in 1922, the father Patrick died in 1926 (daughter Sarah A. is informant), the mother Bridget died 1937 - daughter Sarah Anne is again the informant. I didn't see a death or marriage for Sarah Anne or the son Michael in the area (the civil registration name switched from Parsonstown back to Birr in the 1920s). There a couple of other Parnell households in the county at the time of the 1911 census - about 25 individuals in all.
Facebook is probably the best place to look for a local groups, I'd check for any for Birr. Many of the groups are private, so you dont get to see what's going on until you send a join request.