First, do not plug the set in (or again). Without replacing the electrolytic filter caps, you can cause more damage to the set.
Next, replace all the wax-paper caps. These can also be "hiding" in the bakelite blocks and metal-cans and tone control assembly. See the bakelite block re-buiilding info on my site:
http://www.philcorepairbench.com/capbuild.htm
Also check all the resistors for proper values. Replace any that are outside the +/-20% tolerance.
Check all RF and IF coils and audio transformers for continuity. You may find one or more open.
Regards,
Chuck Schwark
The Philco Repair Bench
You may also want to check the resistor and mica cap connected from the detector's cathode to ground. If one opens or the cap shorts out, the detector may stop functioning properly. This would also give you no audio, but the hum may be louder.
By the way, there are three versions of the Philco 90: One with push-pull 45 output tubes, one with a single-ended 47 output tube, and one with push-pull 47 output tubes. Which one do you have?