So when I started playing guitar a couple years ago, I bought one of those small, cheap Danelectro Honeytone Amps. As an aside, I was amazed at the nice, warm, rock n roll growl tones I was able to get from it with 9 volt battery, play with it clipped to my belt "busking" around my house. I had no real "ear" or anything to compare it to, but my gut told me I was getting good bang for the buck, and 2 years later I still agree, amazing for $20.

Well, after a couple months, one of them stopped working, and got put in a "fix it" box for last couple years, have not gotten back to it till now. (For the record, the other one is still going strong, so I guess some are built better than others, as with anything.)

I don't know electronics, the notion I could "fix" this is maybe too ambitious? On the other hand, maybe taking apart and fiddling with a tiny amp like this would be a good starting point as I start to get more into electric guitar, fx, amps. I mean, I'd like to learn to be one of the guys who can custom / mod / fix his own gear one day.

So, back to this fix it job. When I turn on the amp, the red "power" light goes on, but I get no volume at all. Is that enough for anyone out there to suggest something to try to fix this? Should I just unscrew it and see if anything stands out to a novice, like a disconnected wire? These things go for $20 new, so it's not economically worth it for me to spend an hour or more fiddling with this, but I'd do it for the education if there's a reasonable chance I could figure it out and learn something. On the other hand, if it's all going to just be way too technical for me to have any hope of understanding, then I guess I'll swallow that down and just "give it a miss" and put this in the "toss or give away" box.

Bernie Sanders for President!
A loose wire is the most common problem. Open her up and have a look.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY
Unfortunately, your description of the problem helps some, but it's not enough. It's obvious that you're getting power to the circuitry. At this point, it could be:

1. Bad speaker
2. Bad wiring, perhaps the wiring going to the speaker
3. A bad amplifier IC
4. Some other failed component on the circuit board
5. Input jack issue

Some of those items can be easily looked at, while others would require some test equipment and the ability to use it. Having a decent schematic would also help. If it's the amplifier IC, it could be an LM386, which is fairly common and easily replaced - with the correct soldering and desoldering skills. Even if it's not an LM386, it's still likely to be fairly common and available.

I'd say open it up and have a look. You can't make it any worse by having a look.