No doubt.
Does anything at all light up on the radio. Meter lights? Channel digits? Any of the Tx/Rx or AM/USB/LSB lights?
Drilling down to what isn't working always begins with a tally of what IS working.
One detail worth mentioning about this radio is the choice of a ground connection for the meter's negative lead any time you want to make a voltage measurement with a meter.
The metal chassis will *NOT* serve this purpose.
At all.
The "-", or negative pin of the DC power socket is best. On the under side you'll see a small coil that goes from this pin of the DC power socket to a tie strip. Either end of that small coil is a good ground for checking DC voltages. Attach the black lead of the meter there before probing elsewhere for a voltage reading.
Since the power switch is not connected to the hot positive side of the radio's internal DC power supply, you will get odd readings if you choose the wrong place for the ground side of your meter hookup. Odd readings that won't tell you (or anyone else) anything useful.
That front-panel on/off button is connected between the radio's circuit-board ground and the negative side of the power supply. For this reason, the usual spots on the radio's circuit board are not a good choice for grounding the black lead of your meter.
Far as I know, the Cobra 2000 is the only CB base radio ever sold that has the power button wired this way on the inside.
73