I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For John Hogarty B 1796 +/- 4 yrs somewhere in Ireland with a father's forename unknown, I found 1 B rcd in 1796 Cork. Rcd keeping at this time was very poor. The chance that it is for your ancestor is abt 5%.
Even though he may have been "pressed" into military service, he likely had a British Military service record. The UK military has rcds dating back to Oliver Cromwell. Find these at one or more of the following: