Thanks for your replies.
Yes, it's the mast that snapped. The Corolla is a 1992 LE and the antenna is in the front driver's pillar.
The coax on the 'donor' wreck was routed high up and toward the cowl, under the dash. After I unplugged it from the radio, it would not pull free. As I incrementally removed more and more of the dash at the wreckers, feesding the coax along, it was still sticking right up to the point where it was finally disappearing into the base of the pillar (in the driver's foot well area).
I am worried that I will need to take apart my whole car to replace this! I am going to attempt the string trick Ray O. Perhaps as a 'fish' I will use some re-bar wire I have here, which won't cut itself on steel corners. Reception is so bad now it won't make any difference.
This is why people use coathangers!!
I wish that I couyld just slide a new mast into the plastic mount at the pillar.
Thanks again,
Jack