Hi Giamma,
If the power supply is working properly, then it appears to be an issue with the motherboard. You may consider replacing it.
If the system is within warranty please share the system's Service Tag and Owner's Name with me via private message (click my username and then click Start Conversation). If the system is not in warranty any more you may contact Dell's Out of Warranty repairs team at 1-800-288-4410 for assistance (Applicable for USA).
If you are in a different region, Go to http://dell.to/18NmI2D select the country/region from the top, scroll down and click on 'Contact Dell Sales' to get the contact information.
Please reply if you have any questions.