Carlos, as long as you have your Data Backed Up, you're half way to having your mind at ease. The first thing to do in cases like this is to make a full back up of all your Data. You've done that, good on you.
Now, using your new computer, download and burn to a CD "Darik's Boot and Nuke", a hard drive disk wipe and data clearing utility. You can find it at http://download.cnet.com/Darik-s-Boot-and-Nuke-for-CD-and-DVD/3000-2094_4-10151762.html, along with some pretty good instructions on how to use it.
Once it's burned onto the CD, take it out of your new computer, and put it in your old one. You may have to go into its BIOS, and change the Boot order to CD/DVD first. When you've done that boot to the CD, it has its own little operating system, and when you select your partition hit F10. That's it, you just have to wait while it does its thing.
The Nuke part in its name is true. Once it's finished all the data is gone. There may be ways to resurrect the data, but I seriously doubt that the technician would have those tools. You will of course lose your Windows XP, but if you have the Installation CD, or at least the Licence Number, he can put it back if you still want it. I hope this helped.
Carlos, I forgot to state the obvious. That is, when you get your now Working computer back from the technician, you can reinstall all your data, if you want to. However, it sounds to me like you should just reinstall your data to your new computer, and find a new home for your old one. But if you still want to use the old one, by all mean, reinstall the data to it.
The one drawback to using this method, is you will lose all your software programs. But as you couldn't boot up the computer to selectively destroy your sensitive data, this is the only option left to you, unless you are comfortable booting up a Linux distro. Even if you were, if your computer wouldn't boot, it's probably a hard drive failure. Then there's not much you could have done, even in Linux to get the drive to spin up, and be readable. All you Linux folks can start to correct me now.
Note: This post was edited by its original author to merge additional information from second post to original response. on 05/01/2015 at 9:22 AM PT