I really don't try to troubleshoot this sort of problem without a 'scope showing what's coming out of the transmitter while it's keyed. And having a 'scope with a probe to see what comes out of pin 1 on IC4 is an unfair advantage. The DC voltage there should be around 4 Volts, more or less.
But the one test that won't require even that much is your finger laying alongside the shaft of a small screwdriver.
Key the mike in AM mode and touch the tip of the screwdriver to pin 3 of IC4. Your finger touching the shaft provides a pretty good hum and noise source into the chip.
This should get you a raucous squeal out of the transmitter's modulation.
If you don't, unsolder the center pin of TR32 so that the lead doesn't touch the rim of the hole in the foil pad, and try again.
If THIS gets you the feedback noises from the "manual digital signal injector", there is a fault in the modulation-limiting circuits.
And if you don't get any noise at all from the pin 3 test, the problem is downstream from that point.
Simply changing parts before the fault's location is established creates the risk of adding a new fault to the first one. If you're scrupulously careful and never create any accidental solder bridges between adjacent foil pads, the risk is smaller.
We have seen a few radios where the owner followed internet advice to "just change" some likely part. When that didn't fix it, the radio comes to us. Handy thing we're good at identifying multiple faults in a radio.
If it starts out with only one fault, the troubleshooting is simplified if no other faults are added to it. Have a very close look at the foil traces leading from where the center lug of the mike pin is wired to the front edge of the main circuit board. We have seen solder faults there more than once.
73