You do not give an indication of his date of birth, but assuming he was under 40 at the time of his trial and was born in Cambridgeshire , then he should appear on the
Cambridge Baptism Index, 1801-1837, which is available on the
Cambridge FHS website.
There are 3 William Cases on this site, 2 of which would have been under 10 years old in 1840 and therefore can be ignored. This leaves one baptised in 1824 at Holy Trinity Church, the son of William & Ann, they were living in Market Street,
Cambridge at the time.