1993 Toyota Corolla revs high and will stay that

Sounds like piston blow by, as the gap increases and diesels have such high compression. When the turbo kicks in, the pressure is restored.

https://www.google.com/search?q=Toyota+Corolla+2+Litre+diesel.+Why+loss+of+power+at+low+revs+when+warm

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If changing the battery does not solve problem, or only solves it until the battery dies then have the alternator tested. I have noticed on several occasions with a couple of my vehicles that at times of very high moisture in the air they do not stay running, once the humidity goes down they are fine.

Your toyota technician should know what a "cold starting solenoid" is. It is the little thing that works your throttle until the motor warms up and something else takes over. I'd suggest going to another technician.

- Check the alternator belt for tightness, carbon brushes, diodes (6) and automatic voltage regulator.

check to make sure the cold start injector is operating. Then look for intake air leaks and vacuum leaks.

AC clutch relay. rockauto.com $11

Get a can of carbureator cleaner and spray around intake, see if idle evens out. sounds like a vacumn leak

Quick explanation of your fuel system:

An automotive fuel system consists of everything between the fuel tank and the carburetor or fuel injection unit. This includes the tank itself, all the lines, one or more fuel filters, a fuel pump (mechanical, electric, or both), and the carburetor or fuel injection unit.
With the exception of the carburetor or fuel injection unit, the fuel system is quite simple in operation. Fuel is drawn or pumped from the tank through the fuel line by the fuel pump, which forces it through the fuel filter, and from there to the carburetor/injection unit where it is distributed to the cylinders.

So with that info...try first to clean your spark plugs.
Next, replace your fuel filter.
After that, depending on a carburetor/fuel injection, try an additive that cleans the injectors. For the carburetor, try a half of can of what is called "Seafoam". It comes in a metal can available everywhere, including Walmart. It is worth the $6-8 and also will "dry" out your fuel from water. Very good product.

After that, get back to us and let us know how your Toyota is running.

Some possibilities:
--the choke cable or the choke linkage on the carburetor is sticking, holding the revs too high.
--the gas pedal linkage, the pedal cable, or its linkage to the carburetor are sticking.
--the engine computer (if it has one) is failing, or has poor connections, or isn't grounded properly.
--various other sensors (if you have them) could be failing.
--the mechanism (computerized or mechanical) calling for more fuel to the carburetor when the air conditioning (if you have it) is turned on could be sticking or not working properly.
You should be able to test most of these possibilities while the car is standing still, with the engine running. Start with the choke -- have a helper move the knob and see if the engine responds properly, especially in the "off" position. Then have the helper operate the gas pedal while you watch what's going on with the carburetor.
Have your helper turn the a/c on and off. If you see a mechanical linkage to the carburetor move when the a/c is turned on, it should move back to its original position when it's turned off.
If any of these linkages (including the gas pedal linkage under the dash) are sticking, try spraying the affected area with a lubricant (like WD-40). If that doesn't help, spray lubricant into the cables, or replace them.
If all else fails, carefully check all vacuum lines in the engine compartment. An intermittent leak (or blockage) could be affecting engine speed.

you can ajust the engine rpm idle from the idle screw and air flow screw on the intek housing