After some digging into RewriteRules and other mod_rewrite stuff, I tried to run the weblog with a clean install (just unzip into new directory and point Apache to it) of WordPress. The comments and single pages still did not show up. So I figured it must be something else. Since I also read somewhere that Askimet (an anti-spam plugin) could be disabled to solve the problem, I did just that.
It did not work. But I also have Bad Behaviour and WP-Hashcash active. Disabling Hashcash brought back the comments and single pages. FINALLY.
I did happen to use an old version of WP-Hashcash, so I’ll check to see if I can use the new version without any trouble.
Thanks for your patience.
Update: I switched from WP-Hashcash 2.3 to 4.0.1 and things still seem to be working.