Carpet on concrete
Well, let me put it this way.
If you're talking about a basement slab that's below ground, you DON'T want to just put a sheet of plastic down. You MAY need to install sleepers and a sub-floor.
However, if you're talking about an ABOVE-grade slab, you're probably OK to just put it right down on the slab (on top of padding, of course, WHICH by the way, I wouldn't skimp on. Concrete is HARD to begin with and DOESN'T 'give' under your feet like wood or a joist-built floor does.)
IN general, it's usually best to allow the concrete floor to 'breath' unless (as I mentioned) you actually have a moisture problem. You can control the moisture w/a dehumidifier that drains into either a sump pump pit or a floor drain. (Forget buying a dehumidifier that has you emptying the water container every day or so.)
If you have more ?'s, post back or e-mail me directly. My best to ya and hope this helps.
Jay J -Moderator
If the former, get rid of those tackstrips and replace them with new ones. If the latter, then bleach the heck out of the floor, the corners, the joints between the floor and walls, and the tack strips, t5hemselves; let it soak; mop it up; and then let it dry for a few days before installing carpet. Once mildew gets a foothold, its spores linger behind, ready to germinate whenever moisture returns. Kill the spores with lots of bleach before installing new carpet, otherwise it will get into your new carpet sooner than you might think.
As "belt and suspenders" protection, you also might want to consider painting the subfloor and joints between the floor/walls with mildew-resistant, glossy paint to which you add a packet of mildicide that is available at Home Depot or Lowes. (I did so in my new place after fighting a month-long long war against mildew that had me ripping walls down.) I have heard that it is against Federal Law to sell paint with mildicide in it at retail (no matter what any can of paint might claim), so you need to add mildicide to paint if you want it.