OK, try this. The tests are processed in this sequence, so you will need to ensure that the sequence is correct.
IF(
[Date Field1] < Today() and not [Check Box 1], "Late",
[Date Field 2] < Today()
and
(Trim([Field1])="", or Trim([Field2])="" or Trim([field3])=""), "Late",
[Date Field 3] < Today()
and not [Check Box2]
and not [Check Box3]
and not [Check Box 4], "Late",
[Date Field 4] < Today()
and not [Check Box5]
and not [Check Box6]
and not [Check Box 7],"Late")
If the above does not pass a syntax check and you can't fix it please post the formula and the error message but copying and pasting into the forum (not a screen shot)