Have you ever thought of the possibility that he could be collicy? (sp?) Does he sleep well during the day or scream a lot during the day? I used the cry-it-out or "extinction" method with my daughter, but not until she was 4 mo. old! I don't know what to tell you, except they say that if you are going to ignore the crying--don't go in there at all--not even after an hour or more of crying. They say you have to let them learn to self-sooth and put themselves back to sleep. This has to last for about 3 nights in a row in order for it to start working. I just don't think a 3 week old should be expected of that... however, I can't imagine what I would do in your situation. Maybe just keep trying what you are trying, but he may eventually get used to that treatment and expect it, never learning to self-sooth. Well, just hang in there... it will get better!
By reading one of the other responses, I remember a few other things I went through:
I made a list of what could be wrong when my baby cried.
1)wet/dirty diaper, 2)hungry, 3)gas (try Little Tummies Gas Relief Drops), 4)needed pacifier, or 5)just wanted held. Like one of the gals said, you'll figure out his needs when he cries!
Oh--and try a sound machine. This is extremely helpful with helping them relax. Turn it on the same sound, same volume every night and they will start to associate it with sleeping!