The capacitors are suspect just because of the age of the unit. These old units used oil and paper type capacitors, so called electrolytic. Paper ages, dries out and can absorb moisture, and the oil may leak. Additionally, the value of the capacitor can change and the unit will not operate correctly. If a capacitor is bad, it will blow and currrent will go right to your transformers. This would most likely ruin the unit.
The cabinet is the easy to have refinshed. It may need to be re-vaneered. Remove the radio ffrom the unit and take it to a furniture restorer, or do it yourself.
Good luck!