most likely the MB3756 voltage regulator is bad.
that, or one or more of the associated electrolytic caps has gone bad.
they are the ones that look like tiny beer cans wrapped in plastic.
You said that this was a Taiwan radio which means that it was made in the late 70's or early 80's. this means that the electrolytic capacitors are either bad, or are going to go bad one by one over the next few years.
The reason i mention this is because unless these are all replaced, you can run around in circles trying to find a problem, only to find out that during your troubleshooting, another part has gone bad. the recommendation is to replace all of them at once, then align the radio. you can find kits on ebay for this.
for now, you probably just want to see if you can make the radio work again,
so, i will qualify my next statements with the fact that you may end up chasing your tail due to one or more shorted capacitors in the radio.
most of the time when a problem like the one you describe comes up, its the voltage regulator itself that has gone bad.
get your DC voltmeter and put the negative lead to PC board ground. (any of the metal tuning cans is good for this)
now put the positive probe to each pin of the MB3756, starting at the pin closest to the back of the radio. this is pin 1.
here are the voltages you should find:
pin 1 should be 8 volts all the time. both RX and TX.
pin 2 should be 13.8 volts all the time. this is the input voltage going into the radio.
pin 3 should be 8 volts all the time. this is just a reference voltage.
pin 4 is ground, and should show 0 volts.
pin 5 is the RX / TX switching pin. it controls the voltages on pins 6 and 8. you will read different voltages on this pin in RX than you will in TX.
pin 6 is 8 volts, receive only. it will drop to 0 when you key the mic.
pin 8 is 8 volts, transmit only, it will drop to 0 when you unkey the mic.
chances are pretty good that one of these voltages is not there, or way off what it should be.
if you find this to be the case, unsolder that pin from the PC board and very carefully bend it up so that it is no longer making contact with anything.
now measure that pin again. is the voltage now correct?
if it is, you have a bad part on the trace on the PC board. follow it wherever it leads looking for a part that is off value. start with the electrolytic caps. you will need to unsolder them from the board in order to test them.
put your voltmeter to read resistance, and put one lead on each leg of the cap.
it may show 0 ohms for a second or two, but should read like an open connection.
if you find one that reads as a direct short, replace it.
really, you should replace any that you pull from the board with new ones just to get a jump on the re-capping.
if you find that the voltage on the pin is still wrong even after removing it from the board, then the regulator itself is bad and needs to be replaced.
the caveat is that there may be a bad component on the board that caused the regulator to fry, and the new one will fry too.
this is where troubleshooting skills come in handy, and i don't have the time or strength to go into all of that in a thread.
you might want to buy two of them just in case if you are planning to try replacing it.
this is a great radio, and is very much worth spending a few bucks on.
IMO the taiwan cobras are the best out there. they are just old and need some TLC.
hope this helps,
LC