Hi Sacatuki! Does the Xbox display any sort of indicator, such as a sequence of flashing leds on the power and eject button, or an error code on screen?
Try powering on the Xbox with a different power cable, on a different outlet in your home. This will rule out a faulty power cable and/or faulty power outlet. The Original Xbox uses a generic IEC cable - you most likely will have another device that uses the same cable, and if not they only cost around $4. If it still doesn't work after that, most likely your PSU has gone bad and needs to be replaced.