Joe,
What it sounds like to me that you need to do is a rim swap. If you have any doubt about the spokes or nipples just replace them. Doing a rim swap is simple. If you can get the same rim superb. What you do is tape the new rim to the old one. Electrical tape works good, it is also thin. Just line up the valve holes and make sure the spoke holes are lined up. Next Loosen all the spokes, then pick a starting point, and one at a time move the spoke over to the corresponding hole. Next get all the spokes hand tight. Then using a spoke wrench (this is what I do anyway) put a round of tension (one full turn) on all the spokes. Next it is time to take the hops out. If you have a truing stand this wiil help alot. If not you can do it in your frame using the brake pads. This will take longer but you can do it. If it hops down tighten the spokes in that area. If it hops up loosen the spokes in that area. Tighten only in 1/4 turn increments. Loosen the same. Now it is time to dish the wheel. Dish is centering the rim on the hub. In the frame yu can measure from stay to rim, on both sides of the rim. However if you have a dishing tool it is easier. Once you have these two accomplished, it is time for tension and truing. I like to true it first then put tension on it. However you can do it vice versa. If you tension it first put the same turn's on each spoke start off with 1/4 turn's until the spokes are not loose. If you do not have a tension meter do it by feel gauge it by the front wheel or rear whichever is already done. Then true it up. Of course if you alreay knew this then maybe someone else can benefit from it.