[Arne]

Both of my PT's have experienced this exact problem.
First a year ago, then the other did it last week.
The troubleshooting was very easy.
When I realized that jumping did not help her at all, I took the positive cable and reached down carefully to the starter solenoid and clamped onto the red plus connection there. Got in, started right up.
In both cases the cable connecting the battery plus post to the starter solenoid main terminal had failed.
You could replace the battery cable or do what I've done.
Leave everything intact but add a heavy, new, short generic cable from the clamp tightening nut down to the starter. takes about five minutes, lasts forever.