To start, I hope you didn't just remove all the caps at once and install the new ones that way. This tends to produce polarity errors, one or more electrolytic caps installed backwards. The faults this could cause are too many to count. Pulling them out and replacing them one at a time reduces this risk. A lot.
And if in fact you:
1)Got every cap with the polarity correct
2)Didn't accidentally "bridge" solder across two separate foil traces that are close together.
The next question would be how did it work before it was recapped?
If it had these exact faults BOTH before and after, this means it has other problems besides decades-old electrolytic caps. Had them all along.
But this is the first important question. Just what did it do and what did the radio NOT do before it was recapped?
That one is a really, really big deal.
Not so different from calling your mechanic and telling him "my car won't start". He'll start asking questions to try and pin down which parts of the engine are present and accounted for, and which are not. As in "does the dashboard light up", "do you hear a "click" turning the key".
Same process for a radio.
Last question. Does the status LED on the front panel change color when you key the mike? You didn't say.
73