try to break a climb like Aconcagua down in parts and get experience on all of them:
- long trip: at least two weeks without any real comfort. This can already be trained by a 10day hike anywhere, just as long as you are carrying a full pack and are camping.
- cold to extreme cold (Mt Washington?)
- physical efforts: long bike rides, long hikes: work up to 5-8 hours of activity. Test your self and know your limits as you will have to cross them with confidence.
- Altitude: this is very hard to prepare for close to DC
Mental preparation is key: know how you will behave in a storm, without hotels nearby.. with not a single tree or other green thing outside for at least 2 weeks... while carrying a heavy pack. Once you are prepared for that and comfortable with it, you can try to climb Aconcagua.
Then you still need luck with the weather of course, but at least you will not be the problem in that case