If you click on the Home > Basement Waterproofing link below your question, you can read up on what sort of issues could be causing your problem, and various solutions - if you read thorugh the last couple of months ones dealing with water problems or basement mold, it should give a you a pretty good idea of possible causes and sources. If the discussions in there do not lead you to deetermining the source of the water, then continue below. It is probably going to take a process of elimination to find the source, THEN think about possible solutions.
If, after reading them, you want to communicste back with more details or questions, use the Submit Answer button below to keep it in the same "thread", and your and each contributor to the thread will receive an eMail telling them there is another post on the subject to look at. If you want to, let us know what town you live in so we can have an idea of likely geology in your area.
From your description, sounds like you have gotten a bum steer and been run in circles in general - new roof and radon venting, for instance, have nothing to do with moisture problems. The only benefit those could do is slightly reduce moisture under the slab if it was just ground moisture (not seepage) you were seeing. New gutters, if properly directing the water away from the foundation, might help if that was the source of the water. If the pipes leading the water away from the house to the popups were watertight and the inlet from the gutter cannot overflow, rather than perforated, that could help. If perforated drain pipe, that would concentrate the runoff from the roof in four distinct areas.
For a flat ground site, drains with popups generally do nothing as the water level is still at surface level when you need to get it below the slab level - unless they drain to a lower elevation than the slab. The french drain is probably the same story - unless it gets rid of the water via drainage to a lower elevation, a pump system, or drywell penetrating a free-draining "dry" layer it will do nothing but concentrate water at the foundation - exactly what you do NOT want.
Look around your area, ask neighbors, etc. to see if there is evidence of high water table in your area - creek or swampy areas nearby and close to your house level, neighbors all have sump pumps, neighbors who have had to put in french drains with drywells or pumps or full-perimeter waterproofing, etc. Ask the engineering department at your local building department, and at your local water/sewer utility, if they know what the water table level runs in your area. If you ask around, you should be able to determine if this is a general problem in your area, or not. If it is, then a wetwell pump system and/or sump pump is likely to the be required solution, and without tearing out your slab to put in an underdrain system, an exposed sealed concrete slab (whcih could be polished, stained, or epoxy coated) is likely to be your only viable flooring option.
Additional topsoil, even if sloped away from the house, does nothing unless it is compacted so it is relatively impervious (and should be clayey soil, not topsoil). Controlling surface water is the solution if it is NOT high groundwater level - both by directing rain runoff and gutter drainage away from the house at least 6-10 feet, and by ensuring any surface water does not pond on the area around the house by installing swales or french drains, as applicable.
You say you had a plumber check for leaks. I would suggest you go one step further - buy a $10-15 metal (not cheap play plastic one) stethoscope at your local pharmacy, and after being sure all water flow is off in the house, do some listening. Do this with any boiler or furnace, AC, dishwasher and clothes washer, bathroom fans, etc off to stop mechanical and any circulating pump noise, and do NOT do when hot water heater is heating, as that will add noise. Then listen to the water pipe where it comes into the house, and at any external shutoff valve or water meter. You should be able to easily hear if you have a water pipe leak - even the tiniest barely visible pinhole spray can be clearly heard through the pipes. You may even hear the pilot flame on the furnace and hot water heater - listen to a pipe right by them to hear what they sound like, then work away toward the outside, or if you know how to relight them safely turn themm off too while you are listening.
I forgot to ask - if you are on a septic system, that makes for a locally high water table, and since you say your ground is pretty flat, could be the root cause also.
If you cannot pinpoint the source with the above methods, then I hate to say it, but I think you need to invest in an on-site conference with a civil engineer specializing in foundation water problems. Probably about $150-300 for a consultation, additional $300-1500 if there need to be a couple of soil borings to determine water levels and soil drainage conditions.