Hi there agabenson,
Didn't know where to start with your family so took a look at the 1851 for them as you obviously had this.
Lynn covers a very large area and the census is only searchable by place name. So I tried South Lynn All Saints as this is where they were in 1851 but there is no sign of them. Saying that there are quite a few pages that were unreadable. The only way you'll find out William's fathers name is to get his birth cert.
Just as a matter of fact there is an entry on the Lds site for a william Hill born abt 1841 parents Richard and Elizabeth it names the other siblings and the ages all fit?
Sorry I couldn't find them for you.
All the best and good luck Angela.