I've been brewing for 21 years, and I still remember how agonizing those first batches were to wait on, especially that first one!
IME, 3 weeks is enough time to carbonate if the room temperature is in the low to mid 70's. Cooler than that and it'll take longer. I think it's too soon to call it a dud. Give it another week and try another bottle.
I didn't use priming sugar. I used carb tabs.