Henry,
I have repaired two of these HP8601 sweep generators within the past year. The two capacitors that you circled control the sweep time and, as you have found out, have nothing to do with the frequency control. The smaller capacitor is A9C1 and sets the time constant for the “FAST” sweep setting. The large, broken capacitor is A9C2 and is placed in parallel with A9C1 when the sweep mode is set to “SLOW”. Both capacitors are electrolytic, not tantalum, per the HP8601A service manual parts list. The slow sweep speed is extremely slow and was intended to drive one of the axis of a pen plotter through the sweep out connection.
Your second scope picture confirms that you do not have any output on the high frequency range.
The service manual is available free for download. Best source for a quality scan of the manual is the Boat Anchor Manual Archive (bama), bama.edebris.com. The bama archive also has a zip file of stitched together schematics which I found to be extremely helpful. The manual is written in the classic old school HP style and includes an excellent troubleshooting flowchart and test procedures for each of the modules. One of the problems with repairing one of these units is dealing with the SMC connectors. SMC adapters are not cheap.
I concur that you start first with evaluating the power supply. Both units I repaired had power supply issues. Both had missing -75V rails which was caused by leaky electrolytic capacitors (A10C11). One of the units had excessive ripple on the +20 V rail which was caused by a bad transistor A10Q5 (Current source, HP P/N 1854-0071). I replaced all of the electrolytic capacitors in the power supply but kept the original tantalum capacitors.
I would guess that you might have other issues besides the power supply. I suspect that there might be a problem with the A1 Discriminator or A2 Divider or some problem with the control signals to those two modules. Only one crystal oscillator and VTO is used for both ranges but the frequency divisor used in the A2 module is different for the two ranges. The A3 Loop Amplifier, A4 Crystal Oscillator and A5 VTO, A6 Amp, A7 Attenuator might be in working order since you have output on the lower frequency range.
Dave