I don't recommend quit attending to you get dropped from the class but that may have to do it

If you've got screenshots, and I'd also go somewhere to check the website to print it out and get a certified copy if you can, then go speak to them in person. If they try to brush you off, point out you've got the copy and if they try to do this, it's theft (assuming you've paid for the class) and they'll change their tune rather quickly. Don't expect help in the future, however. They'll likely remember you embarrassing them. Always copy any documentation, record any meetings, etc, to cover your own ass.

If they don't let you drop it just don't go to any classes

Maybe you can talk to the professor of that class and get a special permission to drop the class. This happened to me once in grad school (I did not drop out from the class before the deadline). I had to take a special permission from my advisor and then approach the Dean of Graduate School. So dropping is still possible.

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I'm sorry, OP. In their defense though, screenshots hardly count as evidence in that sort of thing anymore. 'Inspect Element' and Photoshop make it easy to fake things. Still a bad situation.

OP here. I know that screenshots aren't very good evidence, but it was basically all I had (since the website had been updated since). I'm on a quarter system so there's not enough time to go with a lot of your ideas, though I appreciate you guys trying. Oh, and I did go to my parents. Not for help, since I did everything possible before I called them about it, but they didn't believe me either. （´・ω・｀） Shit just sucks sometimes.

Go in to the registrar's office in person with your evidence. I went to a community college for some Gen Eds and, when I transferred to a university, I had to request my transcripts from the college through a website and I selected an email transcript (so it would arrive sooner) and that it be sent to the transfer coordinator. We waited for about four months, all the while emailing them, trying to get my transcript. Eventually, I had enough and complied screenshots of my confirmation that said I paid for it and who it was supposed to be sent to, emails from three people saying it had been sent, and emails from the transfer coordinator that she had not received it into one document and then emailed that to myself. The next day, I went down to the school, had my document ready on a tablet to show them, and, at first, politely explained my frustration that it had not been received and that I'd like an official paper transcript. The lady I was speaking to told me I'd have to request it (and pay for it again) online through their website service to which I told her I already did and that it was never received. After I got the runaround a few times and me not budging, she got a supervisor. The supervisor tried to tell me the same thing - that I'd have to request it online -I told her I already did, it was never received, and then I showed her my document of screenshots, as well, and told her, also, I wasn't leaving without a hard copy of my transcript. I got my hard copy transcript which I promptly dropped off at my university to the transfer coordinator. TL;DR: I couldn't get transcripts from a community college, collected evidence into a document, and refused to leave without a hard copy transcript. I won.

Use archive.org it has a historical record of website changes

Sue them