Selecting the next empty cell in a row / vba

Hello and thanks to anyone who can help,
I am using Excel 2002
The code below works fine except I want to select the next empty cell to the right in the row each time the same player's score is entered.
As it reads now, it just overwrites the previous entry.


Sheets("Classic").Select
ActiveSheet.Unprotect

Range("B1").Select
Do Until ActiveCell.Value = Player.Value
ActiveCell.Offset(1, 0).Select
Loop
ActiveCell.Value = Player.Value
Activecell.offset(0,4).value=Score.value

ActiveSheet.Protect

GameNumber.Value = ""
Player.Value = ""
Score.Value = ""

Hoping someone can assist,

Regards,

Oscarr