radio antenna problem

My 1996 Jeep Cherokee S****t just developed a problem.  Overnight the
radio went from being pretty good to one that gets nothing but static.
The tape player works fine.  My first thought was the antenna came
unplugged from the radio.  I pulled off all the plastic crap and
pulled the radio.  The antenna was plugged in.  I stuck a piece of
insulated wire into the female antenna connection and got good FM but
no AM reception.  So, I assumed the radio is OK and there must be a
problem with the coax going from radio to the antenna.  I measured the
resistance from the tip of the connector that goes to the radio to the
outside antenna and got high resistance - several megohms.  The
resistance from the outside of the coax connector to ground is high as
well.  Is there any solution other than replacing the antenna coax?
My guess is that the resistance for both should be only a few ohms.
Right?  Is it reasonable that the antenna coax would go bad like that
overnight?  Is the coax one piece from radio to antenna or could there
be some connection that has come lose?  How hard is it to replace the
coax (without completely removing the entire dashboard)?  Oh, there
have been no accidents or traumatic jars to the car other than a few
holes in the road.  Right now I'm driving around with all the plastic
in the back seat and my jerryrig antenna wire laying on the dash.
That's OK with me but my bride doesn't like it.