Simply assuming the problem is a dud sensor is a great way to replace a bunch of things that weren’t causing the problem. This needs to be diagnosed and the first step there is to have the car electronically scanned to see what faults the computer already knows about. From there, you can make a much more informed plan of attack.

That said, you may well be right and the problem is a crank-angle sensor or something to do with the throttle position sensor. But, equally, the problem could be with the car’s wiring (getting hot when the power is turned on) or the fuel pump, so making a guess and replacing that component is a great way to waste time and money. A scan is quick and cheap and the smart way to go on any electronically fuel-injected vehicle.

Plenty of used cars change hands without service books in the glovebox. But this is usually a problem in older cars where the vehicle is well and truly out of warranty. In a newer cars such as yours, the lack of any service history in the car would be a major red flag.

There’s no law requiring a car dealer to provide a service history, just as there’s no law compelling owners to have their cars serviced correctly, even though failing to do so will often void the car’s warranty. And how can a dealer be responsible for a car’s service books if the previous owner lost them? Also, if the car hasn’t been serviced within the Toyota dealership network, how can a dealership determine what that service history has been?

But here’s what’s probably happened: Many dealerships (especially high-volume ones) remove the service handbook, owner’s manual and the second key from the car before it goes on the lot. That’s to prevent those things going 'missing' over the weeks the car is on sale and being test driven by who-knows-who. In my experience, there will be one person at that car-yard who will know where the books and keys and stored and until you find that person, their location will remain a mystery. But, if the car was bought on the condition that the service books would be sent to you, then that forms part of the contract of sale and the car-yard must produce them. In the meantime, since you don’t know when the last service was carried out, I’d be pushing for a free service to ensure the car doesn’t wind up with a skipped service based on time and kilometres.

On older cars like this one, some pretty strange electrical things can start to happen as switches and wiring ages. The first thing to check for is that there’s not a cargo area or interior light staying on when it shouldn’t and subsequently flattening the battery.

But the failure of the stereo and temperature gauge both point to a body computer problem (as does the battery going flat). The body computer basically controls all the car’s functions that are not driveline related. So, the central locking, lighting, entertainment, security, power windows, climate control and much, much more are body-computer driven. And if this computer fails, lights can turn themselves on, the central locking can cycle over and over again and various other electrical bits and pieces can switch themselves on and drain the battery.

But there’s one other check to make before blaming the computer (which, on a 1994 Corolla, won’t be as complex as one on a more modern car), which is to make sure there are no bad earths on the car. Failing gauges are a common symptom of a bad earth somewhere on the car, and if that’s the case, you might find this is also causing the starting problems by not allowing the battery to fully charge when the car is driven.