iPhone not being recognized by computer

Should do as you say. When you plug it in, does the phone power symbol show that its recharging at least ?

Did you make sure that Apple Mobile Device Service is installed and working? http://support.apple.com/kb/HT1747

Your music should be in your itunes library, but having a backup of it is always a good thing.
Reinstalling AMDS should not delete your music on your computer.
Before you try to connect to your powerbook, make sure autosync is disabled in itunes.
If you manage to get the iphone recognized in itunes, back up manually:
Right click on your phone in the device list and choose backup.
This will save data, pictures taken with the phone and settings to itunes.
See what's included in this backup here: http://support.apple.com/kb/HT1766
Transfer your purchases the same way to copy all apps and bought media from the Store to your computer.
Set up at least one contact and event on your computer to be able the merge your calendars and contacts after your phone got wiped during the first sync.
The rest of the data can be restored from the backup you made.
Restoring: http://support.apple.com/kb/HT1414