Lisa, I'll send you a private message too just to make sure you get it, but posting on the message board because others might like the info too.
www.rootsireland.ie is quite a good resource. You do have to pay to actually get a transcript of the entry, but can do quite a bit of backgrounding by looking through the indexes. You can even be sneaky with it if you have a lot of time and an uncommon surname by narrowing down to parish, and then going through the alphabet as the first initial of first name. This worked really well for me when I actually knew the parish for one person, and wanted to see if any siblings there as well. I then managed to keep to a reasonable budget for actually getting the transcripts and out of 8 that I had guessed at, 7 were actually mine!
So, Lisa, the ones that might be relevant to you are a number of James Sinnotts in Wicklow around 1833. If you don't have a better idea of the parish or of any siblings, then it may not help. There is one for 1834 which is probably the closest, but I wouldn't count on it definitely being yours - I have found too much discrepancy in dates given in UK censuses in my own ones to be that specific about it. The confusing bit with yours is that there are also three more James' in 1830 and one in 1835, and at this stage I would say that any of the six could be yours.
If you want to see the actual records, then the microfilms are in the national library in dublin. Its well worth a trip there, once you have a bit better idea where you are looking. I had a few preconceived ideas and it wasn't until I returned home that I realised where one of my assumptions was wrong and so I have missed the potential to go a lot further back. Still, there is always a next trip!
If you have money, then the Wicklow Family history centre will do the research for you and write you up a report.