You should have antivirus software installed on the new computer that can scan the iphone for viruses etc. before any sync takes place, if that is what you are worried about. Just plug it in.

If you aren't worried about plugging it in, but still don't want to sync and the iphone is out of warranty, jailbreak it. Access the iphone's file system and copy & paste your photos to the external drive (this may require renaming).

If you can't or won't do either of these, look for an app that will allow you to send them all straight to the PC via WiFi. If you are stuck e-mailing them, look for an archiving app (like WinZip) that may help cut down the number of files you have to attach.

Not sure about the music - I would delete the itunes library and reinstall the software. I assume you have tried playing the files in another player to verify that they aren't corrupted?