Parameters in queries are limited. You're getting the error because of the combo box reference. Also, it looks like you would want to do an update statement not an append. Try doing it in VBA like below. I'm assuming that your combo box is grabbing a numeric value, if not you would need to change "intAsset" to a string variable.
Code:
Dim dtStart As Date
Dim intAsset As Integer
If IsNull(Me.txtStart) Then
MsgBox "You must enter a date"
Exit Sub
End If
dtStart = Me.txtStart
intAsset = Me.cmbAssest
CurrentDb.Execute "UPDATE DriversHistory SET DriversHistory.endDate = " & dtStart & _
" WHERE Asset= " & intAsset & " AND endDate is null"
Dan
Access Development