[Blue Bowtie]

First, the terminology.

If the engine started/ran briefly with the application of starting fluid, it fired. In order for that to occur, the starter must be able to crank the engine.

Reading between the lines, it would seem that the electrical system had some sort of failure and the battery power was insufficient to crank the engine, thus the rapid clicking of the starter solenoid.

Some time later it was jumped to a vehicle with adequate power, and apparently cranked without starting, otherwise even a wild guess at insufficient fuel pressure would be irrelevant.

Finally, if the engine did start/run for a few seconds after the application of fuel (starter fluid) it would seem the ignition system is intact and fuel delivery is indeed in question. There can be many reasons for this, from an empty tank or clogged fuel filter to a failed fuel pump or security lockout. It will be essential to get a good, fully charged battery installed (or fully charge the existing battery) before diagnosis can commence.