Recently, I moved to a new state. The previous place I lived was full of conflict that made my parents hate the place. I had a job and "spent too much time there", " wasted " my money buying things off Amazon, told my parents that I want to be a girl (and an really confused in terms of sexuality), and had constant power struggles with them. Granted, I did a lot of stuff I shouldn't have during this (like storming out of the house after exploding at my mom about something, and going behind their backs for many things), but they did their fair share of wrong too. They isolated me to the point where I hated being home, took away things I liked too much rather than help me use them responsibly, asked me "what right did I have" when I told them how bad I was feeling, and generally made very little effort to understand me or have reasonable conversations with me.
However, one incident that stands out in my memory happened one dark night when I walked out with the intention of walking into the ocean and never coming back. They picked me up, ranting about how "it was on me to save my family" (relationship-wise). Then, when I told them off my intentions, they actually said "how dare you". And we aren't even the kind of people who believe suicide is a sin. And the next day, when I told my counselor at school and asked for help, they yelled at me for doing it.
Forgive me, but in my eyes, they just lost my respect and trust. (I lost theirs years ago. We never really got along all that well.)
Now that we moved, my mom is completely denying what happened there. Like, when I brought up how I had a doctor's diagnosis with depression, or said it might be a good idea to keep going to a therapist, she said " I told you we aren't doing that here!! Here isn't going to be another South Carolina, and if you want to do that you can just go back there right now!! " She also frequently accuses me of "not trying" and talks about how she's doing everything different (read: letting me watch TV or play with the dog out keep the phone I bought behind her back). But she's not really doing anything different where it matters most.
And I don't know what to do about this. Because it seems that anytime I criticize my parents (even without being rude) they go on the defensive, or else shut down the conversation. Things aren't good. And I'm not sure how to talk to them about this. Does anybody have any advice?

No answers, but a thought or two for consideration.

One note is: if it seems like suicide is the answer, you're asking the wrong question.

wrt parents ... well, examine some why it is they reacted so badly to the thought of you (it was just you, right?) seeing a therapist.  Suicidal thoughts and actions are not something many parents are in a good position to deal with.  Therapists are in a better place for that.  So from my great remove, and not knowing much at all, it does seem like a good idea for you to see one.

In referring to criticizing them ... well, parents are, alas, people too.  Not all people are good about receiving criticism.  For more sensitive people, which it sounds like they are, you might want to try a different line of approach entirely.  I'm assuming that your criticisms are aimed at them doing things differently than they have been.  If so, then it can be helpful to talk more in terms of "I'd like it if you would X", X being something concrete like use this pronoun or name for you, or knock before entering your room (and wait for a positive response), or whatever.

Key in this wrt sensitive people is to not add the thing(s) they're doing wrong.  Not even to say "I'd like it if you would X, because Y (that you do) makes me feel bad."   Just talk about the better things that you'd like them to do.

No guarantees with this path either, but it seems like maybe a different one than you've been trying.  So maybe different results.

The way I see it is you only have two possible paths. One is to open a line of communication with at least one of your parents. Not understand exactly what is going on, I really can't tell you what to fix, but if the conversation is to happened, your parents will have to see you as an adult and not a child. They could be seeing you as a child because of your behavior or because they aren't ready to let go of the child image in their mind. In either case, you have to make your parents believe your are adult enough for that type of conversation
The other path that is open to you would be through your school. Your school many be able to provide some therapy or connect you with social services that could provide you with help. If you take this path, be aware that you family might not be very happy about this level of interference in their life.
Sometime a church or somebody else in the area could also provide help, but as you are new to the area, you probably don't know of anyone else you could ask for help.