If much of anything has gone bad in a 16 yr old dishwasher, it's not cost effective to repair it, as it's at the end of it's life. Before you give up on it, I'd check and make sure water is getting pumped out. I recently had a problem with mine, where dishes suddenly weren't gettin cleaned well. Turned out to be a partial block in the drain line, so only part of the water was getting pumped out each cycle.
So, I went from figuring I was gonna spend $400 on a new dishwasher, to thinking I was home free. Then I found a corroded out brass drain pipe under the sink. While fixing that, I noticed the disposal was a little loose in the sink. Being 16 yrs old, the release nut wouldn't budge and I wound up breaking that, so now it's time for a new disposal. Then, I figured now that I've gone this far, I've never been crazy about the sink, so now's a good time to replace it. After a week in sink hell, I finally found the right Kohler cast iron one that I really like and it cost $400. So, the whole thing is now costing me $600+. I guess I would have been better if I had needed a new dishwasher! Then, after getting the sink special order from HD, I lug the 100lb behemoth home, put it in the counter and then notice it has a spider web cracking in one upper basin corner. Back it goes.....