Do you have a recent database backup of your site? You could just use that (a kind of pave and nuke option admittedly).
Unfortunately I only have an XML backup, not a database one. 🙁
Let’s test something first – go to your permalink settings and select an appropriate permalink structure and click save/update. Doing this will flush the rewrite directives (basically WordPress’s instructions on how to route URL requests to the right resource/page/post) and refresh them. Does that fix things?
See, that’s the thing– when I switch over to one of the other permalink structures, everything on the main page breaks, which is why right now permalinks are all on the default setting.
Is there some special settings on the theme side? You said that the Fragment theme is a “one-page” theme – I’m wondering if it has some settings for links that need to be reset?
Other things to try, turn off your custom theme and enable a default WordPress theme and change your permalinks. Then re-enable your old theme and see if that fixes things (assuming any of your customizations won’t get lost when disabling and re-enabling the custom theme).
See, that’s what I’m wondering too– but I looked around and I don’t see any settings for links to be reset. I almost think that it’s possible WP Mobile Detector inserted some weird code and screwed everything up.
I already tried resetting my .htaccess, but that did nothing.
Okay let’s go back to basic troubleshooting.
1) Disable your custom theme and turn off all plugins (this will only be temporary). Use a default WordPress theme (twentytwelve, twentythirteen). Now go to your permalinks settings and hit save/update. Everything work? If yes great, move to step 2. If not, then something is likely messed up on the server – either WordPress core files have been modified (not likely based on you saying you re-installed WordPress 3.6.1) or something has been misconfigured on the server. Check with your host in this case.
2) Okay so the basic default WordPress setup works. Now re-enable your custom theme. Does everything still work as expected? If yes, great, move to step 3. If not, your custom theme is doing something wrong. You will need to carefully look over your code, possibly in the function.php file of your theme, to see what it’s doing as far as URL redirects. This will require a willingness to read through code and understand the gist of what each function is doing (or asking questions).
3) Carefully re-enable your plugins one by one. If the problem appears again, note which plugin you last enabled. Get your particular environment specs noted (server/hosting specs, WordPress version, theme, plugins, etc.) and contact the plugin developer and let them know what you’ve found.
Anyway, by the end of this you should have a pretty good idea of where the issue is.