You don't say where in the world you are. All English-speaking users can read and answer questions here, no matter whether they are reading yahoo.com, yahoo.co.uk or any other international yahoo portal. It's a quirk of the system. It also means that unless you bother to include your country in your question you will get some very strange answers, some of which will not be relevant. I'm going to assume you're in the UK because that's where I am, and that's where most of my genealogy knowledge lies. If you're in Australia or America then I'm probably doing all this typing for nothing.
Some things of course don't change. Very few countries in the world have any official birth records that begin before the mid nineteenth century - sometimes even later. England and Welsh records began in July 1837, Scotland didn't follow suit until 1855, and Ireland even later. In America, different states started keeping records at different times, but again, rarely this early. Seeing as you are outside of what we call "civil registration", you have to turn to the other great force in peoples lives besides the government, and that is the church. The church keep very good records, which in England and Wales at least can in theory go as far back as 1538. Some don't. Natural disasters such as floods and fires have damaged some records, while others went missing during the commonwealth gap and civil war period covering 1649-1660. Others still, despite recent efforts at preservation, have become to faded after several centuries to make out, even under specialist UV lamps. The survival of such records is therefore something of a lottery, and this assumes that the family you are after weren't non-conformists or anything. Also, some vicars were quite diligent in their record-keeping and made extra notes, while others were less obliging. A baptism record normally wouldn't include a date of birth (traditionally this should have been within three days of birth but the rule wasn't always enforced), and a burial entry wouldn't normally include a date or cause of death unless it was otherwise unusual (a murder, accident or suicide). The vicar usually made a note about the paternity of illegtimate children in his register, especially if there was ever likely to be any chance of a reputed father being chased through the poor laws for maintenence. It is these records that you need to consult, but generally speaking they are not online - again it is something of a lottery as to whether you will strike lucky in a google search.
Armed with a printout of the 1851 census you should hopefully have a good idea of your ancestors claimed birthplace. That is the church at which you should look for a baptism. Hopefully it will be a small rural village church and quite easy to search. Searching in large cities like London can be much harder, especially without an exact birthplace.
Hugh Wallis' website at http://freepages.genealogy.rootsweb.ancestry.com/~hughwallis/IGIBatchNumbers/CountryEngland.htm gives some indication of what records the mormons have on their IGI database at http://www.familysearch.org/eng/default.asp . As you can see, it doesn't include all parishes or all years, just a mere fraction. If you're lucky, a transcription of the record will appear there. If you are unlucky, then it is always worth googling for the local County Family History Society and see if they have transcribed the records on CD for purchase - many of them have. The key here though is "TRANSCRIBED" - volunteers (many of whom in the case of the Mormons aren't even English) trying to read old records and handwriting as best they can. Mistakes do occur. Therefore, the serious genealogist will not just rely on these transcriptions, but will go to the nearest large library or record office and view the original registers on microfilm for themselves, just to check that the entry has been transcribed correctly. This is where problems can kick in. You've reached the limit of what you can do on your PC, and now you find out you have to travel halfway across the country to view the original church records. Sadly, very few people live today in the same area that their ancestors came from originally - I certainly don't - mine are spread north, south, east and west and plenty of places inbetween.
Again, the Mormons might be able to assist you if you have one of their Family History Centres near you as for a small change they can usually order in the church records for you to look at closer to home. Again though, it means getting up from your PC screen and doing some old-fashioned legwork.