This is 99% chance of a gas strut failure. It's a simple fix with only a few fasteners that need to be loosened. Good luck!
and the windshield a window shield. 
I think my car is missing something.
trunk window
Burning Brakes
Joined: May 2004
Posts: 1,182
Likes: 14
From: POINT PLEASANT NEW JERSEY
Definately the two gas struts holding up the rear window. Word of caution...make sure you have at least another person helping you when removing the old ones. That rear glass hatch is super heavy!!! You'll be surprised at its weight!!! When purchasing new struts...shop around..... If original GM parts are important to you than you will pay top dollar..... I recently replaced mine with an aftermarket pair I got on Ebay for like $40 .....they are just as good as GM....don't waste your money and pay the double $$ for lining the GM silver pockets!!! 
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Drifting
Joined: Oct 2006
Posts: 1,694
Likes: 0
From: Beaverton Oregon
I replaced the Hatch Struts for my '89 Trans Am - picked up new ones at my local Outdoor/Sporting Goods/Auto Parts store, known as GI Joes in the Pacific NW. They have a wide variety to choose from. Cost? $30 each.