How to fix partially broken trackback, pingback?

So, I’m trying to get trackback and pingback working for my WP blog (WP 2.0.6). Here’s what works and what doesn’t:

* In Options, I’ve enabled allowing trackbacks and pingbacks.

WHAT’S WORKING:

* Manual trackbacks to my blog from http://kalsey.com/tools/trackback/ get through.

* Trackbacking other blogs from my blog usually works fine.

WHAT’S NOT WORKING:

* Automatic pingbacks to my blog from other blogs seem not to be working (but how do you know?).

* Neither internal pingbacks (automatic) nor internal trackbacks from one post on my blog to another does not work (i.e., if I link to an earlier post it does not automatically get pingbacked, and manually putting the trackback URI in the “Post” trackback field doesn’t work either). The pingbacking post claims to have sent a pingback, but the receiving post does not display it.

* It used to work. When migrating to WP, I used the default theme, and internal pingbacks worked. Switching back to Default now, the problem remains. So I guess the problem is not with my theme. And I’m still on the same host

Given that it works partially, where should I start troubleshooting?