The good news: Except for the music, my files are backed up on various cards and flash drives.
One might wonder why this stuff wasn't all backed up before. Well, the music and programs were, except that then my laptop wasn't working well with the old external hard drive, so I tried to reformat it. Only after this failed several times did it dawn on me that maybe it was the laptop, not the hard drive, at fault. I am thinking I had a decent backup of all but recent data (and I have the recent data), and I foobared it.
I did a back up to cards and flash drives, but did not have enough space to get all the music, let alone the programs. mnemex points out that I am probably better not backing up the programs, but reinstalling them from scratch, given that we're not quite sure what gives.