TL; DR How can I go about either convincing this unwilling advisor or others in my department to keep me despite poor performance?
*Thank you so much for your comments. It's beyond valuable that you are taking the time to read and share opinions. *
Background: I started PhD in management in a reputable institution in US, immediately after undergrad in a small university in Europe. The system works much more differently than I was used to and now I have invested all I can to this area. However, I lack prior experience in research, and especially when changing areas like this, need to develop very specific skills that were hard for me so far. Now I'm pretty beaten up and discouraged by potential advisors to go for a PhD.
The catch is when I applied, one senior faculty jointly appointed with this program and others was my primary "advisor"-candidate- and a second one supported this. Now, the second one has left the institution without any progress with research; and no one else in my department with similar topics is willing to advise me or fund any research I want to do. Without guidance or funding, this seems like a no way out. I really love the research the primary "advisor" is doing and want to continue on the topic I am in, but the topic is not the most common to find among researchers in my field.
My primary "advisor" is already planning to work with other students and my funding is not covering more than tuition after this first year. I really need someone to support me, and help me figure academia out as my first year was really bumpy. The department liaison and chairs are encouraging me to drop out and keep their money in...