In nearly all cases the reset problem is caused by two things, heat expansion of circuit boards inside the DC and poor electrical connections.
This is what happens inside your dreamcast and how it causes your DC to reset.
As you know the dreamcast takes the main supply voltage straight into the back of the system, and this voltage (240v Europe, 110v America) needs to be stepped down and converted to a stable DC current that the electronic components can handle. As the electricity enters your dreamcast it passes through a step-down transformer which reduces the voltage, unfortunately step-down transformers generate heat and as things warm up they expand, the step-down transformer in the dreamcast is located on a separate circuit board, the main power board, which is on the left hand side in the dreamcast above the main mother board and to the left of the GD rom assembly, this is why the left side of the dreamcast gets warmer. The main power board is connected to the dreamcast mother board by six aluminium pins, as the power board heats up it expands slightly putting pressure on the pins and over time this will bend them slightly, resulting in a poor electrical connection that will cause your dreamcast to reset at random.
This is what you do to fix the problem.
You will need the following :
a screwdriver with a + blade
some common sense
and make sure that your dreamcast is out of warranty as the following will void it.
1) Disconnect from the power outlet, remove all cables from the dreamcast and any game disc that's inside
2) Remove the modem
3) Undo the four screws in the base of the dreamcast and KEEP SAFE
4) Remove the lid. On the left hand side you will see: the Main power board, with the GD rom assembly to the right, the input port circuit board at the base, and in the bottom left hand side you will see the power on/off switch, this switch is connected to the power board with a grey cable, at the power board end of the cable there is a white conector, grip the conecter at the base and lift clear.
5) Undo the two brass screws that hold the power board down and KEEP SAFE
6) Towards the base of the power board you will see a white connector, it has six pins sticking out, gently lift the power board out of the dreamcast and off the pins.
7) Under the power board there is a clear plastic insulation sheet DO NOT REMOVE THIS, IF YOU DO PUT IT BACK.
8) Look at the pins and clean any dirt off them. DON'T USE ANY LIQUID to clean them with
9) GENTLY apply SMALL amount of pressure to pins pushing them towards the back of the dreamcast, DO NOT BEND THEM, JUST APPLY A SMALL AMOUNT OF PRESSURE
10) Re-assemble your dreamcast and the resets should be gone.
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http://www94.pair.com/jsoper/dc_fix.html)