I'd like to share what happened in my case because I've seen few people on the internet with the same problem. I've lost few hours on this, I hope it's going to help someone...
Basically, my problem was the following:
I followed golden432's walkthrough, everything went fine and I even got the confirmation that my phone was now rooted.
Then, the phone rebooted and I found the superuser app on it, BUT I clearly couldn't install any apps requiring root (like Titanium Backup) because the phone wasn't rooted (100% sure).
I tried 5 times golden432 walkthrough, everytime it went well from A to Z, but the phone wasn't rooted.
So basically, I did the following things and I don't know which one corrected the problem but it finally worked. I honestly don't have the time to test them all to isolate what really fixed the process.
1) I uninstalled Unlock Root version 3 and installed the version 2.3 instead from this exact link (look at the italic "Downloads required" line) :
here
2) While having the phone plugged in the computer, I went into Device Manager, right click on ADB Composite interface (under Android), and force the reinstallation of the driver. Also, I force Windows XP to take the driver I was selecting, and not to take the best that it could find. The driver I took is the file "android_winusb.inf" located in this package:
here
I am 100% sure that it is the same driver that was installed, but who knows what the forced update did...
3) Then, I ran Unlock root v2.3 and this time I accepted to install the battery saver app that they propose during the rooting process. I don't think that it matters, but since I am listing everything I did differently from my 5 previous tries, I'm including it here.
Then, Unlock root reacted exactly as the previous 5 tries, but this time after my phone rebooted, it was really rooted.
My advice for any beginner would be to follow golden432's step-by-step walkthrough, but to use the files available in this walkthrough: (look at the italic "Downloads required" line) :
here
More info:
Vendor Id of my phone = 0x1C9E
Everything was done on a Windows XP Sp3 computer.
Note: I never suceeded at installing the drivers properly on a Windows 7 Ultimate x64 computer.