@Robert S. sorry you're experiencing this--I've been in your shoes, and it's no fun.
Luckily, I have extensive experience with this type of issue (I learned the hard way when I bought a property that was basically built above a subterranean river that caused three basement floods in about six months!). Incidentally, the property I had that had this issue was also in Salt Lake City; so, I'm familiar with your area.
As you probably know, water in the basement will start to produce mold in about 24 hours, so your first order of business is to get the basement dry ASAP.
You can pay a flood mitigation company to do this, but it will be expensive. You can do it yourself; the process isn't terribly complicated and doesn't require much technical skill, but it is a lot of physical labor, and you'll probably want to get friends to help. You can find videos/articles online on how to get the basement dry, but the basic process is:
1) turn off all electric to the basement (to avoid electrocution from the water),
2) run pumps to get the standing water out of the basement (sounds like you're already doing this)
3) remove all furniture and items from the basement,
4) once you've pumped out the standing water from the basement, rent a wet/dry carpet cleaner/extractor from home depot, and use it to extract as much water as possible from the carpets (they'll be much lighter and easier to move once you get the water out).
5) After you've used the carpet extractor to get most of the water out of the carpet, remove all carpet and get it out of the house for drying (if you're trying to salvage the carpets), or throw the carpet out. If you're trying to salvage the carpets, you'll need to get them bone dry in under 24 hours to avoid mold--so, it's a race against the clock to get them dry fast. If you can get the carpets in direct sunlight, and under industrial-strength drying fans (more on that below), you may be able to get them dry. If it's still raining outside, if you can get the carpets in a garage and under industrial drying fans, you may still be able to get them dry.
6) if the water soaked any drywall, you'll need to cut that drywall out and throw it out.
7) rent a bunch of industrial drying fans from home depot/lowes (they are specifically designed to dry up houses that were flooded, and soaked carpet. They're usually blue, so they should be easy to spot at the home depot/lowes rental desk); put them throughout the previously flooded areas of the basement, and all around the soaked carpet you've removed (if you're trying to salvage the carpet). If you're trying to salvage the carpet, turn the carpet over once every 3ish hours, and keep the fans on the carpet for 24 hours until the carpet is bone dry.
8) rent an industrial dehumidifier from home depot/lowes, and run it in the basement for at least a day or two until the humidity of the basement is low. If the upper floors of the house seem humid, you may need to rent multiple dehumidifiers and run them throughout the house.
Follow these steps quickly, and if you can get the basement dry in under 24 hours, hopefully you can avoid mold. Home depot/lowes sells mold test kits you can use once the basement is dried out.
Once you have the basement dry, the next order of business is to figure out the cause(s) of the flooding, and hopefully address those causes to prevent future floods.
There are multiple potential reasons for your flooding--it could be ground water rising up from underneath the house, it could improper drainage around the house, it could be cracks in the foundation or slab, it could be water coming in through the window wells, it could be all of those things, or it could be something else entirely.
Once you know the reason(s), for the flooding, then you'll be able to figure out a solution.
I'd also strongly suggest that you don't re-finish the basement until you've determined the cause of the flooding and fixed the problem (last thing you want is to re-finish the basement, and have it all ruined again by another flood).
I'd suggest first watching some videos on youtube on flooding, drainage, groundwater, french drains, sump systems, water catchment systems, etc, just to give you a better understanding on what can cause flooding, and what types of fixes might work.
A few questions might help you figure out the cause:
How much rain (or snow melt) was there before/during the flooding?
Does your house have rain gutters, and if so, where are they draining to? Do they drain into the areas of the yard that are flooding? Do they drain into areas near the flooded window wells?
Are there slopes/hills that drain water towards your house? Is there a driveway/patio/other solid surface near your house that would drain water toward the house?
Is the water in the window wells rain water that's falling in from above, or is it ground water that's seeping up from below the window wells? (or perhaps both?)
Where does the water seem to be entering the basement? Is the water in the basement solely around the flooded window wells, or does it seem to be coming in from other spots? FYI: groundwater raises and lowers (it usually raises after periods of rain/snow melt), and if the slab of the house is too close to the water table--that is, if the slab is too low--ground water can rise, and seep up through the slab from underneath the house. Although this is probably less likely than the water leaking in through the window wells, it is possible, and you'll want to eliminate it as a cause of the flooding before deciding on how to fix the issue, because if it's groundwater, then the solution to the problem may be completely different than if it's water coming from other sources.
As you consider these questions, keep in mind that water follows the path of least resistance--for example, water will flow through a gravel-filled trench much quicker than through solid earth/clay. Obviously, water flows downhill. So, water will be attracted to areas that are porous and/or downhill. Keeping those principles in mind, you can better understand why the water is flowing into some places and not others, and from there you can design sump systems/french drains/water catchment pits/gutter systems, etc. to force water to flow away from your house (for instance, a french drain will attract water and carry it away from the house. A sump pit with lots of gravel surrounding the sump basin will attract water much quicker than a sump pit with less gravel around the basin. etc.).
When I had my flooding issues, I paid a hydrologist to come out and inspect the property and educate me on how water was moving around the property, and importantly, how water was moving underground near my foundation. It cost me a few hundred bucks, but it was money well-spent, because it helped me understand how to design the flood mitigation system...rather than approaching it via trial and error, I was able to build a flood mitigation system that worked the first time, and the house hasn't flooded since. The hydrologist was located in Salt Lake, so let me know if you want their contact...
Let us know if you have questions.
Good luck out there!