because I am an ordinary person, I have no facilities and the ability to introduce this algorithm
Typically people write a paper and submit it to a journal. If it's any good and indeed "has no similarity to any other existing algorithms", it will definitely cause a stir. Most methods that you and I can come up with, have been thought of and are either used in modern encryption or were discarded for good reasons.
this algorithm may also have weaknesses that would question its validity
That's a good thing to acknowledge! I remember when I invented my first encryption algorithm: I thought it would be unbreakable as long as it remained closed source (it'd be licensed to banks and stuff). I was super naive as a kid :)
Note that my personal story ended with me putting it up on some forum for security experts and someone breaking it despite not having the algorithm.
the website was created solely for testing this algorithm
On your website, I do not see the algorithm. How are we going to test and validate it?
the algorithm will be publicly released if approved by experts in the field
If you really want to do it that way, you can find and pay said experts to vet your idea. I'd advise you to just post it publicly and see if anyone can pick it apart. Only if there are no glaringly obvious flaws, you might want to have some experts look at it. And actually, if it's indeed good and new, experts will probably be attracted by themselves.
despite repeated attempts and correspondence with reputable technology websites
Wait, crypto experts typically do not reside on technology websites. You'll be wanting to contact consultants and show them green stuff that they can use to exchange for bread and cheese at local stores.
nobody was willing to help me.
They might have recognized that you are at the wrong address, or if you weren't, they'll have gotten many requests from rookies that wanted to validate their neophyte algorithms. Many rookies go down this path of (1) self-inventing things that are stupid and (2) not knowing how to publish. Myself included. I'm not saying that you are a rookie, but it's just likely that you are and people will often not find it worth their time to look at.
Crypto is seen as a hard field because it is indeed hard to do properly. It's not something that comes to you while in the shower, but typically requires years of study. By then, you will have seen how others published their work, so you'll know how to publish. Also, others might have seen your name already if you've been active in the field, which also gives you more credibility to start with.
Please guide me and help inform this.
Release the algorithm and ask some hacker friends to take a go at it for fun.
And optionally, write a paper and try to get a journal to publish it. This should get it reviewed by others from the field.
By the way, having a bounty (as it's called; it's not a bonus) is nice. It'll definitely attract people to look at it. Just be prepared to pay out!
It's a little off-topic (your question is "how to introduce to the world", not "is it secure"), but if I may comment on your video and challenge:
Looking at the video, you're not entering any password. From that I assume that the key material is either (1) hard-coded in the program, (2) written into the output file or (3) does not exist (i.e. the algorithm is the key material). In case of option 1, that's bad practice; option 2 means it's just not encryption (it's encoding); and option 3 means you've violated Kerckhoff's principle.
On the other hand, I'm happily surprised to see that your challenge file has good entropy. When turning the ascii decimals into binary, ent gives me 7.93 bits/byte (for 3099 bytes of binary; testing with 3099 bytes of /dev/urandom I get 7.94 bits per byte). It's at least of better quality than what I invented when I was younger :).
