Let me start off by saying that my job is likely not in jeopardy.

I'm in a "long term contract" position and have been there for 14 months. I brought up wanting to get hired on to my team leader, who is a liaison to my "boss" (who figures out how much our department can spend and who is hired or fired, etc.) many months ago and my TL was on my side for wanting to get hired but said she would get back to me on it. I also expressed that I'd like to take on new or different responsibilities or roles, or at least that I was willing to, because we were experiencing a lot of downtime at the time and I wanted to be more productive. So I had a meeting with the "boss" recently and the company merger went through, so I figured that since I've been there a year and the merger is over that I should be able to get some concrete answers about what I'd need to do to get hired on.

Well I started off saying that I was happy with my job and my work. (there has apparently been some doubt as to whether I'm happy or not because I have been coming in to work later and leaving later and I'm not supposed to do that because staying later is not as safe. I am working on that. That behavior had been happening for a while and I was still getting work done and getting 40 hours in but someone recently noticed it. So that's a problem of mine but I am fixing it.) Then I said that my only wish is that I can get hired on. The boss said that she wasn't considering a third person in my group to be a full time position and that there were other positions that she would prioritize above mine. I think there may have been some more conversation but I don't remember the order. She mentioned that I could spend a day a week in a different department so I could explore my options, most of which are lateral moves, and I have followed up with her on that to specify which department I'd be most interested in even though that feels like I'm being juggled around. It's an opportunity to improve my skill set though and it seems like something that she wanted me to do even though that was only vaguely hinted and not specified that "hey if you do this you can get hired on." At some point we got on the hiring-on topic again (since I don't remember the order I don't remember if we were still on topic or had switched topics) and I said "I just don't think it's fair that, you know, I've been here a year and the merger's over and I'm in such a small group (group of three) and I'm doing the same work as my team members but I'm still a contractor and they're full time employees of [this company]." I am 90% sure I heard her scoff at me. Then she proceeded to explain that my coworkers had different responsibilities and professional duties. (which she's right, they put together a quarterly report, do a presentation on what our group did for the year, and they do some company self-evaluation thing once a year. I feel that I could do that. I don't do it because I didn't even know about the presentation until a week ago and honestly our TL has basically been doing the quarterly reports for the other two team members. I know this because one coworker has asked her how she made the chart for the report to make it look nice and stuff like that. I have never been asked to write the reports because as a contractor I am not expected to, and one of the coworkers doesn't help the other write the report anyway most of the time.) My coworkers have also been with the company much much longer than I have. I responded that I would be willing to take on those responsibilities and that I would like to develop the communication skills that they use in the extra duties that they have and she either once again said that she wasn't prioritizing my position to be full time or went into the other types of development suggestion in different areas of the company.

Until now I didn't even think about how saying something is not fair is stupid to say and now I'm just wondering how I could have phrased that better. I want to get hired on but no one seems to be able to tell me how to go about that.

I've been told by my contractor representative that they are pleased with my work, so I don't really know what to do except start looking for full time jobs with a company or contract to hire positions with a timeline. I like my job enough that I could bear staying there for another 10 months. But I am slowly starting to hate it and I'm getting really bored. I really just want to make sure that I can afford health insurance next year and that I can start getting some vacation time. If I got that and only inflation raises for the next year I'd be happy enough to stay there for five years because I like the job I'm doing more than most of the other jobs I'm qualified to get.

TL;DR: I told my boss that I didn't think it was fair that I was still a contractor after a year and that I do the same work as my coworkers who are employed by the company. I received a cold response. How can I better phrase things to figure out what to do to get hired on, OR should I just give up on them ever hiring me on and look for a new job?