Those are just additional conditions for your WHERE clause, which you should separate with the AND operator, since you want them all to be true if the row is to be updated, as I provided in my previous reply -- just change the "!=" to "=" (SQL uses "=", not "==" as a comparison operator).
... WHERE phonenum='$phonenum' AND value1='' AND value2=''
If you want to separate the logic to process each field separately based on whether or not it is set (or NULL), you could use the IF() function:
UPDATE mytable SET
value1 = IF(ISNULL(value1) OR value1='', '$value1', NULL),
value2 = IF(ISNULL(value2) OR value2='', '$value2', NULL)
WHERE phonenum='$phonenum'