WITH THE DC INSTALLED*
Use alligator clips with 2 AA batteries or 3V. Attach them according to the following diagram, the positive lead on 1 the negative lead on 3. The Game Boy should turn on regardless of the power switch. If it doesn't, there may be an issue between the battery contacts and the DC board or with the DC board itself.
Testing the DC board:
With a multimeter, test the voltage of pin 7. You should be getting a reading of 5V. If not, the DC board is dead.