http://www.segagagadomain.com/hardware/treamcast.htm
Pic does show draw of 30 watts. Your model might be different power rating.
30 watts divided by 12 volts = just over 2 amps not quite 3 amps needed.
To play it safe make sure power supply is at least 3 amps feeding to the TC.
Try to get a good 12 volt car battery, it will be a solid confirmation on power issue. (has plenty of amp reserve)
If that fully charged car battery doesn't work then its definitely not the power supply.
Can the LCD screen be disconnected from the Treamcast? Without a lot of cannabalizing that is. If so try removing the monitor may be able to tell if monitor or dreamcast half is bad. Even that little power slide switch could be marginal. You could temporary hook up bypass (that switch) jumper wire internally.