My iPhone 3G has died. Is there any way I can access its contacts data either in my Mac or in my HP PC that I used to sync it with, before I get a new iPhone (which may be some time)?
Since you have a Mac, you should've selected Address Book to sync. You should also start setting up a gmail account in the future and also sync your contacts there by exporting from Address Book, so you always have contacts in multiple locations.
Address book should indeed contain your contacts unless you didn't select to sync them back to your Mac. If not, you'll have to restore from backup with a new phone to recover them.