I got the same error (80030416) when I was searching for media servers. My PC was previously sharing media just fine with the ps3, but after I installed a new game the media server was gone. Or then it had something to do with the fact that during the installation I added a file to the list of shared files. Feels strange though since the installation and file sharing shouldn't be related in any way.
I've seen this one a few places, but nobody seems to have a good description: 8002F14E
It is encountered during firmware updates. From my experience, it's indicative of a blu-ray drive issue. In my case the drive was actually not present -- borrowing my friend's drive and putting it in my PS3 allowed my update to complete.