Every document we've found on running Linux on the Thinkpad 600E says that ALSA sound works best, and you should use the CS4236 driver. ALSA's own alsaconf tool says, "Aha, you have a Thinkpad 600, we detected a CS4610 chip, but even though we detected it as a CS4610 you should use the CS4236 driver."
All this information would be a bit more relevant if ALSA HAD a CS4236 driver ... it appears current versions, both within the kernel and as a separate download, don't contain one. Neither do the kernel OSS drivers.
The commercial OSS package from 4Front Technologies does, and it's now completely free for home/personal use so long as you refresh it every 4 months. If that is too much hassle, you have the option of buying a "permanent"¹ license for $50. The latest version, OSS 4.0, is offered only for 2.6 kernels, however, and only as an RPM or a Debian package.
Update: 4Front says that when the final release version of OSS 4.0 ships next week, there will be a .tgz package. In the meantime, I made one from the rpm using alien.
[1] The license never expires, but allows support for one year and licensed upgrades to new versions for 2 years. By comparison, I don't really see a refresh every four months as a problem.