There is a pot on the laser sled-- a gray one-- and it was turned down way too low. Now the laser attempts to read all the way across my audio cd, from the spindle out, only to get to the very outer rim of the disc and then fail.
Keith Courage offered to try his hand at fixing mine, and I'm just going to take him up on the offer at this point; I've already sunk a good six or seven hours into this and still don't have it working.
Thanks to everyone who has given me troubleshooting advice!