In a circuit that combines 35 MHz with 7.8 MHz, to obtain 27 MHz neither of those numbers appears meaningful.
Are you using a digital 'scope that tries to count the displayed waveform's frequency?
If so, those numbers are most likely bogus. A digital 'scope requires a minimum input level to display the correct frequency. And the waveform must have only one frequency in it.
But a mixer circuit's function is to combine two frequencies.
What we're interested in is what comes out of IC5. If the inputs at pins 11+13, and the other input at pins 7+8 both appear healthy, the output at pins 2+3 should have a larger amplitude.
Since you can hear a signal in the handheld radio, you know the mixer chip is doing its job, combining 7.8 and 35 MHz. The signal is getting lost somewhere downstream from IC5.
A radio with an S-meter allows you to see if the tuning slugs on L45, 46, 47 and 48 each respond with a proper peak when adjusted. If they do, that circuit is probably okay. And if you can't get a proper peak from that slug, it indicates trouble in that circuit.
The tip of a 'scope probe tends to disrupt the peak adjustment of those coils when it touches the circuit. Best way to check those four in a 'dead' transmitter is with a receiver. It won't disrupt the peak adjustment of a coil slug the way a probe tip tends to do.
The behavior of those four slugs can be a major diagnostic clue, but not when a 'scope probe's tip is touching one of them.
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