What should a leader do to change a negative corporate environment into a positive one?

It is the leader's attitude and their ability to communicate the values they have. Stating that is a start and communicating it constantly is important. I have a values statement created with my team. We researched company value statements and choose the ones we thought were most important. Each person has a framed copy at heir desk. I have a signature on my e-mail that rotates each value so as I send out mail the values stated right below my name.

Second is taking the power to define the roles for people and making it abundantly clear that they have choices. They can choose to leave. I often say I don't need to fire everyone. I just need to fire the one worst example. By the way in my 27 years I have only fired one person. Others I have discussions and they quickly realize that they should move on. Surprisingly they usually are very happy after they have left as they realize their style just did not fit with the team's style.

The values of my team are as follows:

Teamwork – Having the self confidence to involve everyone and behaving in a boundless fashion.

Quality & Integrity – Having a passion for excellence; paying close attention to consistency, accuracy and detail; and the courage to challenge inaccurate data or the inappropriate interpretation of data.

Technology & Expertise – Committed to utilizing the best technology and being the leaders in knowledge and skills.

Flexibility – Seeing changes as opportunities, so as our customers’ needs change, strive to fulfill these new needs.

Creativity – Making our company an enjoyable place to work and nurturing creativity, dreams and imagination needed to fulfill our goals.

I believe positive energy is contagious. So the leaders need to be positive minded, then he/ she will recruit a like-minded group around him and together they can spread that "Can-do attitude" around. More over, if there are negative thinker in the team, after given chance to change but they don't change, GET RID of them

The only way is change the leader or the leader have to agree to make the change!

The leader should start making money, or having the financial means to make the changes (a raise in capital) if already profitable.
Negative feelings for a whole company comes from not seeing hope and bright future.
But also, not being rewarded for results. This is exactly what happens at an international hospital near you. No profit, no reward on hard work, best doctors leave, new promising doctors dont come.
After the vision of the company is set, align the rewards with the expected results.
And "just-do-it" stop promising!
Read "Elephants can dance" Louis Gestner making the sinking Titanic IBM profitable in just 2 years