Not exactly a vintage amateur radio, but it is about 30 years old.

I'm wondering if anyone has knowledge of how to fix problems with it.

My problem is an intermittent one. Sometimes, when switched on, the S-meter is hard over to the right, as if the RF gain had been turned all the way down. Over a period of a few minutes, the meter will gradually drop down, and eventually the radio will start receiving. After that, it works normally.

Any ideas?

I assume you have tried very careful technical taps around the metering, IF and detector sections.
If not mechanical, perhaps a dried up electro on the AGC.
Time to get the circuit out and study metering section. And detector section.
Not familiar with this model but most are such a pain to find yourself around the various sections.
The more I look at your question, the more I lean towards, IF and Detector section.
JJ

Apparently that model has a reputation for poor through-hole solder joints, so it might pay to check out the boards under a good light and magnifier and re-flow anything that looks suspect.

The signals panel on the bottom, which has the receiver circuitry, is single-sided. The board is huge, taking the entire width and breadth of the radio.

I may as well tell you the repair history of this transceiver.

1. Firstly the power supply, which is poorly designed, blew up. Apparently a common occurence. This was repaired by a friend.

2. Then the power supply fan ran slow, and I discovered the transistor that controls it is barely turning on. Still not fixed.

3. A design problem is the 5 volt regulator on the CPU panel fries the entire board due to heat. It was moved to another area before damage could occur.

4. The flouro display became intermittent. I found that both tracks from the filament socket to its transformer were open circuit, on the CPU panel.

5. The dial lights in the meter blew, another common problem. It needs 28 volt globes, but I had spares. Or you can use 2x 12volt in series.

6. The battery holder broke, still not fixed. The backup capacitor only lasts a few hours now, instead of a week.

7. The sliding door over the batteries jammed, still not fixed.

8. The transmitter started outputting spurious powerful carriers, so I resoldered every flow-through joint on the PA board.

9. And, this is the last problem, with the receive AGC at full at power-on, but it's intermittent, and goes away after a few minutes.

Despite all these problems, mostly caused by poor design, the radio itself is excellent, both on receive and transmit. Like most CPU-controlled items, there's lots of unused facilities built in but not hooked up.

G'Day Robbert.

Those thin grey coax cables that push into the sockets on the various PCB's. I have had issues with them in the past on different Kenwood radios, I have a TS-940, which had a few problems caused by those connectors either a film of corrosion between plug and socket or poor soldering.
lots of dry joints on the boards, I bought the 940 dead, well not truly dead, there was lights and display, but no RX or TX, It is a Japanese 110 volt model, That was sent to as a gift to a computer importer amateur radio operator, in the container shipment with the computers, when the TS-940 first came out.
It took a few days to find the dry joint that was causing the issues, Lots of board and component tapping, but it works a treat now and still going strong after a few years.

This site may help with a few of the issues you have ???

https://www.kkn.net/~k5tr/ts930fix/w6nl930.pdf

As a BTW, I heard recently that another issue that can occur with the TS-930S is overheating, due to the mains transformer primary on some of them being designed for 220V.