Well, lagers do take longer as a rule, because of the cooler fermentation. I've never heard that yeast stop working in three weeks- I'm not sure where you heard that but that's not true.
Usually, for a lager, I make a HUGE starter, then chill to 48 degrees. And pitch that into the 50 degree wort. It sounds like you shocked your yeast quite a bit- taking cold yeast, putting it in warm water (don't do that!) and then pitching it into warm wort, then chilling it. Just let it be, and when it's done, you'll know.
Just relax and let it finish up. It's working, albeit slowly, so it's alive and plugging along. Next time, you'll have some different techniques to help it along before you even brew the batch. But for this time, it'll be fine.