Before you start, make sure the power to the fixture is off (not just at the switch) and, if possible, confirm with a non-contact tester (a few bucks at a hardware store).
D are the screws that need to be put through B, which is the bracket that will be attached to the ceiling box to hold up the fixture.
To see which holes, align the bracket with the holes in the fixture base. Thread screws D through the back of the bracket so the threaded ends stick out front. Which side of the bracket is the back depends on the ceiling box and whether you need the offset on the bracket sticking down or up. (It often doesn't matter.)
C are the screws that hold the bracket B to the ceiling box. Once the bracket is installed, you can connect the wires on the fixture to the wires in the ceiling box (including the ground wire to the green screw on the bracket).
Place the fixture against the ceiling with the threaded ends of D sticking through the holes. Attach with the nuts E.
The threaded tube on A is screwed into the center of the fixture, the nut is then tightened down the tube to the fixture. The remaining parts are removed. After bulbs are installed, the globe is put on, followed by the soft washer, the hard washer and the next nut. Don't overtighten or you can crack the globe. Then the decorative cap is put on and then the ball finial.
It sounds like this is what you're describing...
If this is indeed what you've encountered, you should remove the grounding conductor from the twist-on wire connector used to connect the white wires.
The only place grounded (neutral) conductors and grounding conductors should be bonded (connected), is at the main service disconnect.
If there are no grounding conductors in the house, it's not that big of a concern. As long as the wiring is done properly, you should have no problems at all. If there truly are no grounding conductors in the house, connecting fixture grounding conductors will have no effect. If you're really concerned about the lack of grounding conductors, you can install combination ground-fault circuit interrupter (GFCI) breakers in the service panel.
This sentence also has me concerned...
I cannot use the metal ceiling box that was being used with the ceiling fan. I can only use the bracket, which is currently screwed into place, right into the "hole" in the ceiling.
Are you saying that the new light fixture is not installed in an electrical box?
If this is the case, you should correct that issue as well. All electrical connections must be made inside an approved, listed and labeled enclosure.
Best Answer
It's not clear exactly what your situation is, and I'm not sure if you have a ground in the supply, or on the fixture, or both. So I'll try to cover all possible situations.
No grounds
If there are not ground wires, do nothing. You're done.
Metal box
Ground in supply, ground on fixture
If there is a ground in the feeder cable, and a ground wire or screw on the fixture. Attach both the supply ground and the fixture ground to the box, using either a green screw or a ground clip
If the ground screw, or clip is not rated to accept multiple wires (most aren't). Use a grounding twist-on wire connector to connect all the ground wires, then attach the pigtail to the box using a green screw or ground clip.
Ground in supply, no ground on fixture
If you have a metal box, a ground wire in the feeder cable, but no ground wire/screw attached to the fixture. Attach the feeder ground wire to the metal box using a green screw or a ground clip.
In this case, when the fixture is attached to the box it should be bonded through the attachment method.
No ground in supply, ground on fixture
If there is no ground in the feeder cable, but there is a ground wire or screw attached to the fixture. Attach the ground wire of the fixture to the box, using a green screw or ground clip. In this situation the outlet may be feed with Type AC or MC cable, and the box may be grounded on the exterior of the box. Or the outlet may not be grounded at all, in which case the fixture ground is useless.
Nonmetallic box
Ground in supply, ground on fixture
If you have a ground in the feeder cable, and a ground screw or wire on the fixture. Use a twist-on wire connector, or crimp connector to connect all grounds together.
Ground in supply, no ground on fixture
If there is a ground wire in the feeder cable, but no ground screw or wire on the fixture. If a fixture strap is used, attach the ground wire to the fixture strap using a green screw or ground clip.
If a fixture strap is not used, leave the ground wire folder neatly in the back of the box.
No ground in supply, ground on fixture
If you don't have a ground in the feeder cable, but there is a ground wire or screw on the fixture. Don't make any ground connections.