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 county, 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 Mat(hew) Murtagh B 1829 +/- 1 yr, Co. Westmeath, with a father forenamed Mat(hew), I found 0 rcds.
For Pat(rick) Murtagh B 1824 ditto, I found 0 rcds.
For Rose " B 1821 ditto, ditto.
For Edward " B 1819 ditto, ditto.
For John " B 1816 ditto, I found 1 rcd in 1816, Coole RC parish.
For Mat(hew) Murtagh M 1813 +/- 3 yrs in Co. Westmeath, I found 1 rcd in 1815, Coole RC parish.
For Ellen Fagan M ditto, I found 0 rcds. This looked like a slam-dunk. You may have the wrong maiden name, or the IFHF didn't transcribe the bride's part of the rcd. It may be worth the cost of a peek at Mathew's M rcd just to see what the rcd'd bride's name is.
For Mat(hew) Murtagh B 1790 +/- 3 yrs, Westmeath, I found 1 rcd in 1787, Delvin RC parish.
For Ellen Fagan B ditto, I found 0 rcds.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.