a friend just had that problem with his, actually. In that case, it turned out to be a bad battery. So if the battery is suspect, replace it and it may fix a few things along the way.
Here's his quote. "about the Lincoln battery and static in radio. It turned out the battery needed replacing...so that part is all OK now." This was monday.. heh.
Otherwise, checking the connectors at the back of the radio is a simple task. the angled divider between the top and bottom sections of the dash (right above the radio) is held in place with a series of clips, just pry gently. (I can take mine off with my fingers) there will be a few screws behind it. The top and bottom halves of the dash overlap here. You may need to loosen the top to give yourself some wiggle room. (more screws, visible, just underneath the front edge of the dash pad) Lastly, get the screw on either side of the ashtray, and that panel should lift off, then it's two bolts on either side of the radio.
that should be pretty close, anyway.. If memory serves, the antenna cable routes down the wiring channel on the driver's side. it is possible you could be dealing with rodent or water damage here. I've had some water problems, but never any trouble with radio reception. the power function of my antenna no longer works, and it's maybe 2/3rds of the way up. Still works fine here in the cities.
Something else to be aware of, although likely not the problem here, is that these cars will have an external amplifier mounted under the rear deck, not unlike our Marks. On my '86, this amp only operated the front four speakers, and the rear two came right off of the stereo. That was before the JBL branded systems though, so yours may be "better"
Also, right now, you should start thinking about great big snow tires. these cars do surprisingly well without them, but with them, they're unstoppable.
Also, if the "automatic parking brake release while in drive" thing is still reliable, it can make cornering during winter driving and awful lot of fun.
I'm sure there's more, but I'll stop here.