All purpose laptop

With my new job I now commute a significant distance and my desktop here should have been replaced a while ago.  I never thought of myself as a laptop person but the reality is lugging a tower around just isn't an option and I do need to bring my PC with me from time to time.  I've been out of PCs for a while(which is why mine is so old now) so I figured a little advice never killed anyone.

Budget: $2400-3000ish

Expectations:  With the old PC being outdated and needing mobility now I am looking for a laptop that can replace a desktop.  A large screen size is important.

Usage:  I am looking for a laptop that can play full HD movies when on the go or play/stream movies to my bigger HD TV and Sound system for when I am home(or at a friends), play the latest games at med to highish settings and also be able to take it to work and be productive there.

I realize that those requirements means the battery won't last as long as most latpops, it will be large, and weight a significant amount.  The alternative is I lug a desktop around when I visit family/friends(who live a significant distance from me now), cannot use it at work, and will only really get to use it the few hours I am home.

Thanks in advance!