A point here - some portables require a hi-z (hi impedance) input to have an antenna work well. A coax input may not be the best choice in these cases.
I agree it could be a ground or antenna issue, but I believe this fellow is in an apartment, so getting a good RF ground is not really a practical matter. I doubt the landlord would allow him to run a wire down to a copper pipe....73 Mike
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A couple of additional thoughts (brrr...sitting in a 18 degree car will really shock your brain awake...)
I would be quite cautious about making a RF ground for a portable like this. Chances are you may expose yourself to a shock hazard, particularly if the ground for the DC isn't well isolated (and in a cheap portable, I kinda doubt it is). If there's no jack for a ground, I'd pass this by. Besides, a good ground for a plastic-cased radio is not likely to help all that much.
One of the most common problems with portables is the wall wart. These can be noisy as heck - withness the comments by hertzian about the Sat750 and the well known problem with the E1. Choking the wall wart off can be done with a kit from MFJ (or if the Shack still carries it...). The easy way to test for this is to run the portable on batteries - if the noise goes down, you know what needs doing.
There are SO many possible sources of noise on HF - whole books have been written on the subject. Some common ones are these CFL bulbs (nice for the environment, some of these are real noise generators - I have one in my condo and can't say a darn thing - wipes out anything below 6 mhz or so that isn't real strong...), wireless routers and modems, many kitchen appliances...the list seems endless. Time for some detective work. Take your portable, collapse the whip and listen on a frequency with nothing on it. Reduce the RF gain, if you can, just so the radio starts to hear its own noise level. Walk around and see what gives you the most headaches.
Loops are a better bet when you're in an apartment or condo - they can reject some kinds of noise, and some have a detachable element so you can move it around and find that sweet spot where things are reasonably quiet. Degen, Kaito and a few others sell 'em, and many are not all that expensive (there are some - like the Wellbrook and AOR models- that are VERY expensive - no point putting something like that on a 390, frankly). There are even some designs you can make yourself with some tools, and knowing how to solder.