Marshall will be very tricky to trace without a specific place of birth as it is such a common name. Norrie may be a little easier.
The 1831 census for Co Derry has survived. No-one named Norrie but there was an Elizabeth Norray in Ferry Quay St Londonderry. She was RC. Then we have 3 Norry households. 2 lived in the townland of Tamnyreagh in the parish of Lower Cumber and one lived in Gorton which is in Glendermot (sometimes Clondermot). All were Presbyterian (pointing to Scots origins). Headed by Robert, Arthur & Oliver Norry. Here’s one:
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Lower_Cumber/Tamnyreagh/15/
So for me that would be a hint as to the areas to search. If you know the family denomination, then you can search the surviving church records (most of which can be found in PRONI (the public record office) in Belfast. Access to the records there is free. This link explains what records exist, parish by parish:
https://www.nidirect.gov.uk/publications/proni-guide-church-records
If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
There are about 70 Marshall households in the county in the 1831 census. Most were Presbyterian, but not all.