Hi,

I would try opening it up and check around the area where the power supply is located.

This guide covers the opening process:

Replacing Sega Dreamcast Power Block (Power Supply)

You will most likely find a burned component in the power supply board. If you own or have access to a soldering iron, you could try replacing the damaged components. Alternatively, could buy a new US Dreamcast power supply on eBay for around 20 dollars and replace it with the faulty one.