Hi, Dave. Looking at the schematic on Nostalgia Air for the Philco 39-25, I don't see a phono input. Maybe somebody added it. How it works would depend on how he connected it. You say the wires sort of join together after they leave the RCA jack: is it a shielded cable as it should be? Then it would look that way. If you could trace the wiring and report back would be glad to comment.
Try this: put your finger on the grid cap of the 75 tube: should get a loud hum which means the audio section is OK.
Be sure the bandswitch is in the "manual tuning" position for the dial tuning to work. Nostalgia Air says this is position two.
As to the electrolytic caps, common practice is to leave the old cans in place for looks and replace with modern electrolytics below the chassis, which are much smaller. Old ones should not be bridged but taken completely out of the circuit. You can get 8 or 10 mfd. at 450 volt, and 15 or 22 mfd at 250 volt, to replace the three caps in the radio. Notice that cap #41, the 8 mfd., does not have negative connected to chassis. The other two electrolytics do. Philco's schematic symbol for the electrolytic represents the negative side towards the bottom of the drawing, as the U-shaped "can" part of the device. They would have been more helpful just using + and - on the drawing. With modern mini electrolytics, the aluminum can showing on one end is the negative, the wire coming out of the insulating disc end is positive. As already posted above, I wouldn't play the radio any more until paper caps and 'lytics are replaced. Don't want to fry that 84 or the power xfrmr.
I hope I didn't spout a whole lot of stuff you already know! Sometimes I get carried away.
Reece