Soooooooooooo... You get a pingback to notify you that someone linked to your home page from a post, and it shows in the dashboard. Then what are you going to do with it?
I mean, what value is it to your blog other than making you feel good when you're alerted that another site has linked to you? Are you going to reciprocate as a result and link to them? Then what should they do with the pingback from you, re-reciprocate?
It's not like the pingback means that Google or any other search engine is including that link in their ranking calculations. The post where the link is located may not even be indexed and therefore not counted.
I have pingbacks enabled, but really ignore them for the most part.
About the best place to check for inbound links is to go to Yahoo! and search for link:yourURL. This gives the most exhaustive list of backlinks. LINK: operator at Google only typically shows a tiny sample of inbound links they know about. Even in Google's Webmaster Tools they only show a sample. They even include links that are NOT counted like NOFOLLOW links and links from pages known to be under penalty. Google doesn't want you to know which links they count.
You shouldn't be focusing on looking at your backlinks anyway. Simply build links and forget about them.