OK here's the layout as best I can put it:

If A3 has a number less than 1040, then I want it to look at A4 to see if a
date is greater than or less than 12/31/03.

If A4 has a date later than 12/31/03, I want A3 to read "DC04", if A4 has a
date earlier than 1/1/04, I want A3 to read "RTONLY".

Now back to A3, if A3 has a number greater than or equal to 1040 but less
than 1560, I want A3 to read "AGRIZ". If A3 has a number greater than or
equal to 1560, I want A3 to read "ADMINS".

Thanks everyone!