First thing first. Find a friend. If you do not agree with the way things work and think the culture, is extremely negative, chances are that there are others who feel that too. So find someone who not only shares a similar mindset but also willing to share your woes also. It will be really helpful to you. Find some one who may share a cup of tea or his or her lunch with you and also trust you to vent about whatever or whoever is bothering you. If you talk your troubles , it will make you feel better.
In case your work related problem is affecting your personal life then need to take steps to protect with negativity. Avoid people who exude that vibe and surround yourself with people you trust. Another thing, try to work with people keeping cordial relationship with co-workers and avoid potential conflict, but do not look for or force lifelong friendship.
Escape route is very important. It is a bit idealistic to change entire environment of your work place. But happiness lies in your hands and that can be controlled by you. When not at work, try to pursue your hobbies and surround yourself with a support system that stand tall with you.
Approach is very important. May be the issue at hand is really bad or may be it is in your hand. But what is important is how you handle it. Be positive you will see that things will gradually start changing..........