I don't have experience with the 2003 Rams, but most windshields are held against what is called the pinchweld with a type of sticky "rope" made of a tar-like material which sticks tenaciously to both glass and primered metal. Generally these things never leak. However, if the windshield has been replaced at a discount place, the morons working at these places sometimes use Silicone to install the windshield instead of the more costly factory stuff. Silicone is not a good material to install a windshield with--in my experience it ends up leaking. However, you make no mention of having your windshield replaced. So I would do this: Give it the old hose test. You'll need an assistant inside the truck. Take a hose and turn it on pretty full. Take your time and direct (don't spray) the water along the lower portion of the windshield/pinchweld joint, then go up each side--go slowly so that if there is a leak the assistant inside can spot it--then lastly go along the top of the windshield/pinchweld. If it is leaking the guy inside will be able to spot it pretty quickly.