I suggest trying an external DC supply to the DC jack on the rear, with the switch in the "DC" position.
If it works, you have AC power-supply trouble. The clock is powered from the unregulated side of the radio's AC supply. If the regulator pukes, the radio stays dark with the clock still working.
The power switch is a common failure, but it has two circuits. Only one of them is connected. A pair of jumper wires from the unused side to the side that's wired up may save you if that's what has gone bad.
This pic was meant to show the mike-socket modification, but the jumper wires on the power switch are visible, too.
And if the radio won't power up from the DC power cord, the switch may be the problem.
Remember that the power switch in this radio is not connected in the 'hot' side of the power to the radio. It interrupts the negative side of the DC-power source from the radio's main circuit board. The usual voltmeter tests will be confusing if you look for positive DC voltage on the Cobra 2000 power switch.
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