Push the pins towards the rear of the console, push quite hard, but don’t push so hard that you bend them though.
Once you’ve got the board off, you can see how long the pins really are. Be careful, only touch the edges of the power board, don’t touch any of the components just in case of causing damage (to you or the console). Now it’s time to remove the power board, unplug the connector at the rear, then undo the 2 screws (one near the front, one near the back), around the middle of the picture below you can see a small plastic grip holding the board, you’ll need to pull this clip out to be able to pull the power board up. On the left hand size of the console you’ll see the power board, at the front of the power board you’ll see a plastic plug with 6 pins sticking up, these pins come up through the power board from the motherboard below. Take the modem off, and undo the 4 screws on the bottom of the console, then take the upper half of the case off (make sure you’ve removed any discs). It should be quite easy to fix, and all you’ll need is a screwdriver.
There seem to be quite a few common problems with Dreamcast consoles, the most common is it randomly resetting itself.