It's a matter of convention.
It is usual to start the first sentence with a capital letter, but it is not completely wrong to start it with a small letter. Furthermore, it is now increasingly common to omit the commas after the salutation, as well as in the sender's and recipient's addresses and the close of the letter.
The use of a capital letter for the first sentence in a letter is especially recommended when a subject line is included, as this comes between the salutation and the main body of the letter.
This is true of British business letters. American conventions may differ; in particular, it is considered correct to use a colon after the salutation.