My rent is 800. My landlord accepted 500 of it by the due date and I had a balance of 300. Can she still charge me a late fee for that month of rent because the 300 wasn't paid on time? Or is the late fee void because she accepted a partial payment?

No, your rent is late and she can charge a late fee.

Think about it this way - $800 was due on a certain date. If it isn't paid in total on or before that date, it's late.

She can legally charge you the late fee until the entire rental amount is paid.

Yes, they may change you the late fee, since the rent is late