A car that is difficult to start could be suffering from, literally, hundreds of different problems. You need to have the car electronically scanned to see if the on-board computer has logged any faults of glitches in the fuel or ignition system. That's the best way forward or you could find yourself replacing perfectly good components without any change in the car's behaviour.

And don't rule out basic stuff like a battery that seems fine but is struggling to turn the engine over as well as supply enough power for the ignition to work properly. Modern cars with electronically controlled major functions really don't like a battery that is slack and cold weather will often show that problem up.

Also, when you say you've checked the fuel filter, what do you mean? Did you replace it or simply do a visual inspection. You can't really tell by looking at a filter how gunked up it is inside, so while it all looks okay, it could still be a contributing factor in your starting problems. An accurate diagnosis will also be easier if the mechanic has more information to work with. So start taking notice of exactly what is happening. For instance, is the car more difficult to start hot or cold? Does leaving it overnight make a difference to trying to start it for the second time that day? Does the ambient temperature have an effect on starting difficulty? Are there any specific noises the engine makes when it becomes recalcitrant? Keep a diary of this stuff... it might save you money.

This sounds like an odd question, but it’s actually not. Not all cars over the years have been fitted with two reversing lights and having just one was legally acceptable. From memory some Excels (and the early Toyota Prius in some markets and plenty of European cars) were sold here with both a single reversing light and a high-intensity fog-light set into the rear bumper. Australian drivers being unfamiliar with rear fog-lights, often left them turned on all the time, dazzling anybody following.

As well as reducing the cost-per-car, having a fog light and a reversing light that were interchangeable made building cars in both left and right-hand-drive form a little simpler (and cheaper) as the same bumper moulding could be used with the lights simply swapped side-to-side.

In any case, by 2009, the Hyundai Excel had grown a second reversing light to bring it into line with other mainstream cars being sold here. Hyundai Australia managed to dig me up a wiring diagram for the FD model Excel (2007 to 2011) which clearly shows the wiring loom to support two reversing lights.

You’ve got a limited budget, which will determine the car you can buy. It will be a relatively old car, so buy one in the best condition you can find, with the lowest odometer reading, a good service history, and the best safety rating. Try a Mazda3, Toyota Corolla, Kia Rio, and Hyundai i30 from 2008/2009.