Failed upgrade to 6.16, other issues now appearing

I have attempted to update from 6.15 to 6.16, multiple times now. I get the semaphore table error every time.
Other forum posts claim trying update.php repeatedly creates the semaphore table, and completes the update. Beyond the error (and the fact that my install is still clearly at 6.15), this all wasn't terribly problematic.

Now, it apparently won't recognize new modules.
I've installed/enabled/permissioned the Webform module. It shows in content types, but if I try to edit the content type, I am shown admin/content/node-type/webform as the url, but I am actually taken back to admin/content
I also cannot actually create any new Webform pieces of content.
I believe this may be related to the failed upgrade, since I have a fairly similar install, including the Webform module running without any issues (didn't bother to attempt the 6.16 update there yet).

I've tried uploading/replacing just the affected files in the upgrade. I've tried overwriting everything. I've tried removing all the files and uploading the new ones. No change. I've also tried to manually select the updates to be applied, and the most recent 2 for core don't show up in the list.

Help? Are there any other secrets to getting this update to work? Any known issues with modules post-failed-update that I should be aware (and solutions)?