[morzh]

>>I plugged (before read about it and saw not to) it in and it gave me a increasing volume hum with no reaction to the volume knob.

Hi and Welcome.

Well, the old college try does not have to result in the radio destruction or your untimely death, so in an unfamiliar field it always pays to ask first and act later.
The above action potentially could've destroyed the radio. It matters not that the previous owner plugged it without the "poof": he did a stupid thing. You do not need to follow it without questioning.

So.

Rule #1.

Antique tube radios are not to be plugged in until fully recapped. Some might argue it is excessive, but this is a safe rule and it works, whereas the other rules are all a gamble.

So, as to what to replace.
Replace EVERYTHING other than mica capacitors. All tubular paper caps and all electrolytics (there is nothing else cap-wise in there, other than the micas). Oh...of course, the tuning cap stays.
Micas are reliable, do not get leaky, and if not physically damaged by soldering, the overmolded mica type is almost immortal.

After this, though it is no longer a safety issue, all resistors that are outside tolerance (20% is OK) also get replaced.

And, now that the radio was plugged in and hummed, this is a good sign as that means that at least all tubes' filaments are intact. This is an AC/DC set, and one tube's filament open means they all will not light up.

After recap and recarb, all tubes are to be checked. Then you could bring it up on a Variac (some folks like dim bulb, I despise it as a poor man's Variac) and see if it maybe even works, or at least somewhat functional.

Let's stop here. Once you are at this point, we can discuss further actions.

PS. As said before, it is an AC/DC set, and it is NOT isolated from the Mains, which could result in a shock and, in some especially unfortunate cases, in electrocution. AC/DC set, wet floor and touching things with both hands don't mix.
I suggest, if you are entering the hobby (this is how may of us did....it would be just that one radio to restore....) for serious, invest (it is not expensive) in an isolation transformer.

Mike.