There is more than one kind of failure that can shut down AM transmit only. The most common are in power stages. In this case, the AM modulator transistor TR34 and the driver feeding it TR35 are a common fault. Better than "checking" the transistor, a couple of DC-voltage measurements may narrow down the list of suspects.
The metal tab of the RF driver transistor TR39 should have about 6 Volts DC on it when you key the mike in AM mode. If you do, TR34 is not the problem.
If you *DON'T* show DC voltage on the collector tab of the RF driver transistor TR39, next probe the center pin of TR34. You should have the full power-supply voltage, 13.8 Volts DC or whatever the power supply is set for.
If you do, probe the front-most leg of TR34. If it shows zero, TR34 is breaking down under load.
And if you have that approx 6 Volts DC, this suggests wiring or a bad mode selector switch.
73