I have a 2002 chevy cavelier, i used the button on the dash to open the trunk, now the trunk will not latch when i close it.

Chances are the striker is now bent from slamming the trunk with the latch latched. My suggestion is take the car to a competent body shop. They might charge a little for fixing it, but wont do further damage.

First thing is to get the trunk open

(Try to push down the trunk lid before pressing the fob)
ok, let's assume you got it open. Closely inspect the bundle of wires that go into the trunk lid. You will find a small section that will flex when the lid goes from closed to full open. That's the spot to look VERY closely at the flex point. You may find a wire that looses contact due to mechanical agitation while previous openings and closings of the trunk ( a million times).
Fix the wire and spray the trunk latch first with penetrating lube then with pure lube. WITH THE LID STILL OPEN check the remote and the dash button and ensure rhe actions actuate the trunk lid solenoid at the latch.

It is usually referred to as a trunk catch.

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There is a small plastic part on the pull down motor that comes in contact with the trunk lid latch. It is most likely broken off.

The latch is most likely the issue. If the trunk is used a lot, the latch is misaligned or a foreign object obstructed the latch from closing. The latch itself could be damaged. Carefully inspect the opening of the latch and look for bent, mushroomed or damaged steel. I would have to see to know for sure, how to proceed.

move the latch up slamming it knock it lower

My avalon 2002 trunk was not opening. The problem was a little switch in the glove compartment was depressed I puched the switch back in and wala everything was just fine again. A lil black switch in the glove compartment. wish u the best.

there is a little finger in the latch that closes when the trunk is closed chances are that the little finger has closed but the trunk is still open... this can be fixed by looking at the latch on the lid you will see a slot with a metal arm in the middle take a screw driver and place it in the hole in the slot at the top. press the button on the fob to open the trunk while your pulling down on the screw driver the little latch should twist letting the screw driver move through the track and pop out now alowing you to close the trunk and being happy again.

trunk latch cable probably needs to be replaced