I lost my iPhone (had it stolen?) a few weeks ago along with several years of text messages, voice recordings, and notes from my best friend I had known since 5th grade who recently passed away. I had always planned to back it up or record it somehow but was only starting to get to it when I lost it. My greatest regret of 2013 is not backing up those texts, notes, voicemails, etc.. Back it up as soon as you can and don't put it off or you may regret it. Thankfully, I had backed up all our pictures over the years, and backed up that back up, but I would pay a lot of money to have that phone back.
As long as you plugged your iphone into your computer regularly with backups on, or joined your home wifi network while your computer was on the network with wifi backups on, it should still be in the backups, which would get loaded to your new phone if you loaded the new phone you bought from the most recent backup.
I had an iPhone 4 with iOS5 and an extremely old version of iTunes. It hadn't synced it in a long time as iTunes had stopped recognizing my phone. Further, windows on the computer I used to back it up on is now not booting at all. I have assumed that all my iPhone data, if any, would be on that computer unless it was saved in the cloud. Is that correct?
EDIT: I also unregistered my iPhone because I bought an S4 and couldn't receive texts from those with iMessage turned on, as their phones were still iMessaging me. Am I doomed?
You could potentially remove the hard drive from that computer, then put it in an external casing and hook it up to a new computer. Then research software to pull messages out of your old backups. You could potentially still salvage the messages, it sounded like they were old ones
If you can recover the iPhone backup files that iTunes created from the hard drive (such as via an external enclosure like unepipe mentions), you should be able to recover the messages contained within. Messages are stored in a SQLite DB within the backup (this is how jwz's script reads them).
Looks like iTunes on XP stores backups at this path: \Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\. That's the directory you need to recover from the hard drive.
Somehow I never considered this. Linux on my second partition actually boots up, so I can use my Linux OS to grab the files I believe. Thanks! I'll give it a shot!