This does not at all sound like a lemon. The fact that the motor starts when it is jumped shows that there is nothing wrong with the electronics inside the car. The fact that the previous battery was condemned for having "failed;" yet a new replacement battery promptly did the same thing sounds like the cause of the problem was misdiagnosed. This situation probably is being caused by a loose or corroded connection at a battery cable.
The way to address this is to disconnect both cables from the battery; and use a tapered reamer type battery cable service tool to scrape any corrosion off the outside of the battery posts and the inside of the cable clamps. The corosion that causes this is usually not visible; but scraping the mating surfaces will clear the problem up. Do the same thing with the other end of each of those cables.
If there are any other points on the battery cables where there is a junction between cables; all of those points should be taken apart and thoroughly scraped clean. It is also essential that all bolts must be tightened so that the parts they fasten cannot be moved by hand pressure. A cable clamp which was casually left loose can shut down the starting. If a cable clamp bolt is fully tightened; but the clamp still can be moved; this must be repaired. A new clamp is often required in such instances. Sometimes the junction where a battery cable fastens to the engine can cause this. Battery ground cables are just as important as the positive cables, and they cannot be connected to dirty parts or to any parts which are not made of metal.
This vehicle originally was manufactured with a ground cable between the firewall and the engine. Sometimes this auxiliary ground cable is removed and discarded by someone who does not understand its purpose. If the auxiliary ground cable is missing; it can cause starting problems or other types of electrical problems.
Some mechanics are not aware of all these issues. Although it may be difficult to tell a mechanic about what they are already expected to know; it may also be the only way to get this situation fixed. So please show this message to whoever works on the car.
One other possibility might be going on here: There is a switch on the gearshift that cuts off the starter unless the shifter is either in Neutral or Park. The "Park" contacts on this switch usually wear out before the "Neutral" contacts do. For this reason; if the car does not start; try moving the shifter to "Neutral" and seeing whether it starts in that position.