Wow, yeah, I don't know if Chris Li had the exact same problem I had or why he's being so cryptic with the solution.
But I'm happy to say that after days of banging my head against the wall I too have finally fixed my problem with this.
At first the question of whether I'd removed Internet Explorer made me remember that when I installed MC29 it had automatically also installed Microsoft Edge at the same time and that was the only other thing that had changed. So I uninstalled that but that wasn't it. (Speaking of which though, it would be infinitely more polite if you'd ask me before you force a Microsoft Edge installation on me completely out of the blue. It's not like it's even completely essential, it's only one of several possible browser options. Meanwhile I have to spend days just figuring out how to connect to your secret secure server to get a simple working MP3 ENCODER.)
But anyway, this comment:
It reports an error creating a secure connection to the server.
That's your best clue.
was indeed my best clue. Googling that phrase led me to multiple possible solutions. But I kept seeing mention of TLS. Finally someone mentioned a similiar problem with an error creating a secure connection for a completely different website and one of the suggestions was to make sure one of the TLS options was selected in Control Panel\Internet Options. I looked in my Internet Options and TLS 1.0 was selected but there was another option for TLS 1.2. I don't know anything about TLS but I just figured the newer one would probably be better so turned TLS 1.0 off and TLS 1.2 on. Miraculously that fixed the problem completely. I've never used Internet Explorer or ever touched those settings in the 10+ years I've had this computer so those were stock settings. Like I said, I have no idea what TLS is or does or why no other program I've used has ever needed TLS 1.2 over TLS 1.0 but I'm glad I finally figured it out. Thanks for all who offered pointers.
The necessity of TLS 1.2 or over should probably be stickied or added to the FAQ or WIKI or something because I'm sure it's info that will benefit others and save a lot of frustration. I was very much on the verge of ditching MC altogether over this.