Could it be this?

34146046

Since

From Hint 4, its obvious that the password is '12345678'
Since he "added" the password to the paper code, the resulting numbers are

9378769
-1514541
28484549
-2202731
which give the answer of 34146046

This is just a continuation of my previous guess, might not be the real answer because it can't explain hint 1

83034934

Since

From Hint 4, its obvious that the password is '123456'
Since he "added" the password to the paper code, the resulting numbers are

21600991
10707681
40706771
10019491
which give the answer of 83034934

Edit:

From this website, its seems 123456 is the most common password.