Like television sets the power in a radiogram from this era may well have a live chassis. It should be connected to the 'neutral' side of the mains supply but may well not be transformer isolated so be careful to not get electrocuted! Even after you power off the crappiest of electrolytic capacitors can give a very nasty 'belt'. Back in the day the advice was always to keep your non-dominant hand in a pocket and to wear shoes with non conductive soles. Leather and black rubber are not good insulators.
Look at all the electrolytic capacitors. Probably the best plan would be to swap them all anyway. Any sign of leakage or corrosion around the seal or around the pins and tags is a sure sign they are failing; also any sign of bulging on the body or across the base is a good indication of failure. If you do swap them you may have to look around for suitable replacements that have the same capacitance, voltage ratings, operating temperature range and (for the power supply) the same power rating as the originals. Electrolytic capacitors that are >50 years old and are very likely to be well below par. This would not necessarily make for crackly sound quality, but a continuous low-level crackling might be noise generated by electrolytic action in a failed capacitor.
Other things to look for is crackliness coming from the volume and tone potentiometers (variable resistors) or almost any cracked resistors or dry joints anywhere in the circuitry. By the 1960's the valves are likely to be glass base valves with B7A and B9G pinouts. If the machine has been left unused for some time the valve pins are likely to have picked up a bit of oxidation which may cause crackles and bangs.
Try tapping around the inside with a well insulated tool - you might well find some sensitive components that will elicit a lot of crackles or bangs. Twiddle the Volume and Tone knobs is that noisy? Gently rock the valves in their bases if that gives a burst of noise
Try the band switching buttons - the switch contacts behind these might well have become a bit corroded and that is a common cause of noise. Switches are notoriously difficult to clean and are almost possible to replace as they are virtually custom components for any particular model.