Many thanks for looking at those records, Frances.
Raymond, I agree with Frances that these are not the correct parents for your ancestor Philip Quayle. You have the Maughold records for him, and nothing earlier.
What you know is that your ancestor was Philip Quayle whose 1806 marriage in Maughold said he was "from Ballaugh". You also know that he died aged 89, of BallaCorteen, and was buried in Maughold on 17 Jun 1858.
The only bapt in Ballaugh in the IGI which looked possible to fit his age at death was Philip bapt 2 Sept 1770 son of William Quayle & Margaret Cowley.
However the IGI also had a 1773 death for this entry, and Frances has found that the Ballaugh register did indeed say that this Philip was son of William. This was likely to be the death of Philip bapt 1770 son of William Quayle and Margaret Cowley, because there were no other bapts [IGI] in Ballaugh for Philip son of William Q within the date range to be called "son of" (i.e. a child).
Obviously the Ballaugh register has missing entries, and this leaves you with no clues as to whose family Philip descended from.
It is unusual to be able to get further back than census records without looking at numerous wills, decrees, parish registers, and land records (not just indexes) either in the IOM or on LDS filmed copies at their Family History Centres. The reason you have the Maughold details is because Tom Corteen transcribed them all from the original parish register, but it is highly unusual to have this kind of assistance.
Looking through the Ballaugh register would give you a better feel for the families, their place names, and their connections, which you can't get from the IGI. Isn't there a Family History Centre you or a relative can visit to order these films?
Quayle was a very common name in Ballaugh, judging by the wills, and you may need to read through a lot of these looking for a parent or sibling who mentions a son or brother Philip in Maughold. It was common for uncles and aunts to be named in decrees as next of kin supervisors when a mother died leaving young children. Finding a single decree like that can give you the whole family.
The William Quayle will which Frances looked at could possibly have been Philip's father because he mentioned a son Philip - however there is now no evidence that your Philip's father was William. There may be many wills which mention a son Philip, and you need one which says from Maughold. It is also usual to find grandparents' wills saying where their grandchildren were living.
So to find Philip Quayle's family there really is no avoiding looking through the LDS films, unless you are able to visit the IOM and look at the films there.
You would make a list from Brian's website of all the Quayle Ballaugh wills starting from 1770 and gradually work your way through them, looking at every will under Ballaugh on each film. You would soon start building up family groups, and spot Quayle references under other names. http://www3.telus.net/lawson/wills/qayl-will.html
If you order the parish register film at the same time you will be able to sort people into family groups, and when you find Philip you will be able to get back to earlier generations more easily.