Normally I'd start with google, but I'm humbly realizing that I'm completely ignorant and unqualified to establish the viability of any claims I find, so I thought I'd ask you kindly people.

I'm not a musician nor a composer. I played a beat up trumpet, poorly, in 6th grade band and put together a few lame tracks with fruity loops 15 years ago. I don't even know how to read sheet music. But music theory is interesting and I'd like to learn more, starting with a good foundation and with the eventual goal of being able to compose something decent in a DAW or MOD Tracker.

I can't carry a tune in a bucket, but I'm able to find and keep a beat, and in general can pick out and follow instruments within a song even when there's a lot happening. Those are the extent of my musical talents, such as they are.

Funds are not unlimited, but I'm willing and able to spend money towards the effort, as I would for any serious hobby or undertaking.

Where does one start? What books or other resources can you recommend?

It takes years and years to amass music theory knowledge and learn how to actually apply it. If you want to go down that rabbit hole, I'd probably learn some beginner piano first, and then get a book or two on music theory (I have no idea which ones are good, just go by the Amazon reviews I suppose). That way you can actually apply the knowledge and see how it works. Once you have somewhat of a grip on that, invest in a MIDI keyboard controller (if you don't already have one) and some DAW software and play around with it. Reaper and Cubase are both great hobbyist DAWs that are easy use, surprisingly versatile, and very cheap. Listen to a lot of different kinds of music, and try to take note of how songs are put together structurally. Find people to collaborate with and learn from. It's a never-ending process, but it's very rewarding.

Go to a used college book store and see if you can get a freshman level music theory text book, preferably with a workbook that isn't filled out yet. Read through things and do all of the assignments. Also get together with another group of musicians as soon as you can on trumpet. I've found the more you play music, the easier it is to apply and learn more about the theory behind things.

Have fun!

Thanks for the suggestions everyone, I'm taking it all in. To redirect a little bit, I have no intent or ambition to be a musician in the sense of playing an instrument. As much as I might like to, I don't have a ton of time as it is whilst also learning about theory and composition, programming, doing art, and my day job. That said, I realize that developing reasonable proficiency on piano is a good tool and a practical skill applied towards composing so I'm not opposed to that, specifically -- I just don't have time to embark on other instruments, and revisiting my trumpet-playing grade school days is probably the last think I can ever imagine myself wanting to do, even if I still had the thing.

I think mostly what I'm looking for is a more formal understanding of musical structure, even if I'm not one for rigor. I don't want to compose symphonies or produce music for demanding but utterly vague clients. When I've worked with DAWs in the past, I know what sounds good and what sounds bad, to me at least, but I get there by experimenting. I'd like to be able to get there by some combination of creativity, intuition, and whatever this musical algebra is that I lack.