If a business was started as a partnership then turned into a corporation, do both parties still own it together?

Each of you is a 50% shareholder, which means that each of you has an equal right to elect the directors of the corporation, and thus to manage the corporation. Neither of you can remove the other from your respective corporate officership, because doing so would require the vote of a majority of the directors. But if both of you are also employees of the corporation -- i.e., on its payroll -- the question becomes more difficult, because as a general matter, the president can hire and fire employees. Ultimately, if the two of you disagree about your respective roles in the corporation, there is a state-law procedure called "deadlock dissolution" that will enable a court to straighten things out and make sure everyone is treated fairly. Most deadlock-dissolution proceedings are settled.