Hi CGL18,
First off, welcome to the Philco Phorum. I have not worked on a TV for a while but here are some givens:
First off, safety is of extreme importance. There are many high voltage, high current points in any TV that employs vacuum tubes and a CRT (Cathode Ray Tube / Picture Tube). These voltages vary from line voltage to somewhere between 15KV and 30 KV. Even if an electric shock is not strong enough to kill you, the body's reaction to the shock could cause you to lose balance or slam into something, casing injuries, possibly severe injuries.
In addition, be extremely careful around the CRT itself. Wear eye face and body protection when handling the CRT. I had an accident with an old 21" DuMont TV when I was a kid. The face plate was off the set for cleaning and for some reason the CRT imploded. I was standing at the side of the set when it happened. If I was standing in front or back of the set, I would have been blinded, disfigured and disabled by life-changing injuries.
Having said all of this, if you do not have a signal generator or oscilloscope, repair is difficult but still possible.
Did the set work or work better before recapping it? If so, check your work. If not, follow TV Man's advice. Almost all sets of this vintage are "intercarrier" stye, where the sound comes off the Video IF stage. Therefore, if you have sound, then signal is getting from the antenna through the tuner and video IF stages.
What model and chassis is this set? Do you have a schematic?
Start out by adjusting brightness and contrast controls. Anty changes? If not, troubleshoot the CRT and associated circuits. Is this the model with the long "umbilical cord" that allows the set to be at your chairside but the CRT to be on a separate table? Check this cable for shorts or open circuits.
Next, make voltage and resistance measurements, starting with the Video Output and CRT, and working backwards. Abnormal voltages indicate trouble with that stage. abnormal voltages for several stages indicate a power supply issue. If you don't have a signal generator, then inject (very low voltage) AC hum, using a transformer, potentiometer and capacitor, again, working backwards from the video output.
I did n0t ever try this, but I remember some of the old electronics magazines discuss modifying a TV set to provide various signals, Video, IF, sync, etc. outputs. It is vitally important that if either the signal generating set or the set under test are "hot chassis" types, then the chassis must both be at neutral potential.
Hope this still helps.
There seem to be 2 different chassis styles for these sets, one is transformer powered, the other is a "series heater string "hot chassis" type. It is also important to note that some CRTs for these sets have only a 2.5 V or near to that) heater.
Here are some links:
Sams PhotoFact Schematic for Philco Predicta Princess from Early Television Foundation:
https://www.earlytelevision.org/pdf/phil..._466-1.pdf
Repair Hints from Early Television Foundation:
https://www.earlytelevision.org/pdf/pred..._final.pdf