I have a Volvo 940GLT / 1991 with B234F engine, AT + AC, and fight the same problem. The Volvo dealer's "specialists" replaced the starter and the solenoid, on my money of course, and wanted to replace many other parts including the inhibitor. This happened almost two years ago and since then I always have the same problem, not so often during winter (when it is colder outside).
Even if I am not a mechanic or engineer I am sure the cause is the overheating of the engine, because of the malfunctioning of the fan clutch. I am sure about this, because I cannot find any other explanation for the fact that (in order to avoid waiting 30-60 mins for the engine to cool down) I use an original and faster method: I always have in the trunk 1-2 PET bottles with water. When the starter is "dead" I sprinkle it with water and in 20 - 30 sec it will start operating.
REMARK: USE PLASTIC BOTTLES ONLY, AS THEY DO NOT BREAK AND CAN BE USED LIKE A SPRINKLER.
As cooling the starter makes it work again, this is only a matter of overheating. This is maybe due to the fact that, when normally cooled, the engine does not reach the critical temperature for the starter and solenoid. Both these items have / must have a lower operating temperature than the one reached under certain circumstances.
I shall very much appreciate any comments on my answer, mainly because I found the Brickboard's website while searching the net for the bloody fan clutch. Even if I am from Bucharest, Romania, I prefer to buy it from the states (or from anywhere else on earth) at a 4 - 6 times lower price than at the local Volvo dealer's one.

There is supposed to be a "Service socket for starter motor operation" somewhere on or near the left fender well under the hood. The Wiring Diagram shows it as a 2-position female plug with one (Pink) wire, going directly to the starter (via the Neutral Safety switch).

If you can find this plug (so far I haven't on my '93), run a jumper from Battery + to that Pink wire. If it cranks then (but still won't from the key), the problem is probably in the Ign. Sw.

If it won't crank from the jumper, it's apt to be the solenoid itself. But before replacing anything, I would thoroughly clean all connections at the starter as well as the Battery Pos. and Neg.
--
Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.

Dear Desperate....,

May this find you well. According to my Volvo Wiring Diagram (TP 3902404, p. 42) 94 940s with an automatic transmission have a "start inhibit switch" located next to the shifter. Two wires - pink and blue - run to connector 166 located (it appears) on the firewall.From there, a blue-green runs to the starter, and a pink (with white tracer) runs to the ignition switch. If this switch shorts, the vehicle won't start.

If this car has a manual tranny, suspicion shifts to the ignition switch itself, which may also have a faulty connection. When cold, there is contact and the vehicle starts. Once the connection heats up, contact is broken, so once the engine is turned off, no re-start is possible, until the connection cools, enable contact to be restored.

Hope this helps.

Yours faithfully,

spook

If it won't crank over, what about the start inhibitor switch on the transmission(pink and blue wire, at least on a 91 940).

I am not sure I understand the problem: it won't CRANK? As in the starter won't turn over the engine when you turn the key?