Is it possible to access my PS3 via the internet or just another remote PC on the same network? I tried typing in the IP into IE and no luck.

Not currently and probably not ever via the PS3 OS. Allowing remote access would open the PS3 to unnecessary vulnerabilities.

It should be feasible if you have an alternate OS like Linux booted. I don't have it installed, but unless they've crippled the communications in some way you should be good to go.

Linux on the PS3 does this already. I have a web server, a samba server, a VNC server and an SSH server running on my PS3 Linux right now. But like the others said, the PS3 OS doesn't do any of this, at least not yet. And from Linux you can't see the Video/Music/Picture files on the PS3 OS partition.

Not currently and probably not ever via the PS3 OS. Allowing remote access would open the PS3 to unnecessary vulnerabilities.

Bummer... so then there is no other way to transfer MP3s onto the PS3 other than to rip CDs with it? .... Besides loading Linux

Bummer... so then there is no other way to transfer MP3s onto the PS3 other than to rip CDs with it?
That is another story (and somewhat the opposite of what you originally asked).

File Transfer from Computer to PS3 Coming? (http://www.avsforum.com/avs-vb/showthread.php?t=779675)

Bummer... so then there is no other way to transfer MP3s onto the PS3 other than to rip CDs with it? .... Besides loading Linux
Yes there is, you can put them on a CD-RW. When in the PS3, go on the CD icon, use the triangle, then you can copy them to your HD. It's easier when they have all the attribute set properly (or they will end up all in the 'Other' folder.

It can take some time to get used too but I've done it myself.