But I finally have found a solution that works; at least for me. So I'm posting here just in case others can benefit from this solution.
Conditions: Windows 7 installed from an upgrade (I know, I shouldn't have done that), Outlook 2007, HTC TyTN II, no Exchange server.
First, and this is common to other solutions, backup your Outlook database. Now close Outlook.
2: delete partnership on your computer and on the phone.
3: Find the mail setup (it's slightly different in XP, Vista and 7). In Windows 7 go to Control Panel, User Accounts, Mail.
4: In the Mail Setup dialog box, click Show Profiles.
5: Add a new profile and make it default for Outlook. This is the key point because, at least in my case, the defective item was the profile, and this is not repaired by SCANPST, nor detected by the repair Outlook option. Even when you uninstall and re-install Outlook, or you delete the Outlook database, it respects your previous profile, so the error remains there, untouched.
6: Delete the older profile.
7: Now when you open Outlook, import your backup database (you did the backup, didn't you?).
8: Connect your phone, create a new partnership and everything should work now. Note: If you try to sync without deleting the old partnerships (I did try this) you will receive an error indicating that the sync profile doesn't exist.
I hope this helps other people who might face this obscure error. I've been helped many times by the solutions posted in this forum so I'm now giving my 2 cents in return.