There are a few possibilities here. The first is that there’s been a failure of one of the battery cables that connects the battery to the car. If one is loose, broken or badly corroded so that it won’t let current to flow, then it won’t matter how many jump starters you connect, the thing will not fire.

A second possibility is that there’s something gone wrong with the key fob or immobiliser that isn’t allowing the car’s electrical systems to fire up. Even then, however, you’d perhaps expect to get a red light on the dashboard when you hooked up the jump battery.

What about the jump starter pack you’re using. Is it fully charged? Is it still working (some of these units die suddenly when you need them the most)? Don’t forget that some battery terminals have a built-in circuit-breaker that acts as a fuse if the car’s electrical system experiences a power spike. These circuit-breakers can be replaced or sometimes reset to get the volts flowing again.

But possibly more likely that any of those scenarios is a battery that has literally fallen apart internally. A battery is a series of cells and, if one cell collapses or fails, the battery effectively stops being a battery as the missing cell acts as a circuit-breaker. At which point, you can hook up the world’s biggest jump pack or jump battery and nothing will happen. Change the battery for a borrowed one and see if things improve.

Maybe Richard Curtis could check the area where he parks his car and moves it to a safer location. Your confirmation of an issue suggests Honda could look at better sealing of their ECU to stop ants from entering it.

Unfortunately it would appear you are dealing with an incompetent or deceptive dealer. Ask to see proof of what work has been done by the dealer, and have them justify their findings to you. I would also take the case to Honda direct and demand head office intervention. Also consider taking your case to consumer affairs.