Ann, You live in that bluegrass country that gets a lot of rain. I see a number of issues. Don't bring in any more dirt yet cause you may be digging a bunch out. Find out where your discharge line from the sump pump goes to. If it is buried, dig around and find the end. It may go to a ditch or somewhere on the back of the property but I have seen some end close to the house and the water just circulates back to the sump. You need to get it pumped away and downhill from the house.
If you had your basement waterproofed, that tells me there has been a drainage problem for a long time and I would not expect a water proof coating on the inside to keep a lot of water out. Also a lot of water could cause your basement wall to crack and cave in from the hydrostatic pressure of the water in the ground. If they put in window wells with drain tile where there is no window to begin with tells me that you have some severe drainage problems and or high water table problems in your area. Make sure the ground slopes away from the house and put extensions on your downspouts to get the water away from the house.
I also don't like the concrete bottom to the window well. Gravel is better. It may work if you have drain tile that the water can run into but you don't. It may be a quick and temporary fix to keep your window wells from filling up by busting up the concrete and putting in 6 to 12" of gravel. At least it may partially drain until you get your pipe unplugged or replaced.
The main thing is the drain tile that is full of mud. Your tile may have been put in before they used a filter fabric around the pipe and then back filled it with gravel. If that is the case, you may be looking at digging up the tile and replacing it. I would suggest a basement contractor, new home builder, or some plumbers may do it. I would talk to a few of them and get some ideas and bids. Around here we lay the tile in on top of the footing next to the corner with basement wall with the connection to the sump going down and through the footing to the sump unless the sump is on the outside which some builders are doing now. Then it is backfilled with gravel for about 12" and then with a light fill material like to keep the heavy gumbo clay away from the wall.
You need to try to clean out the drain tile first. I would get a drill with a long bit or wood stick and then use a hose with a high pressure fitting on the end (like a pipe and nozzle used to go under sidewalks and driveways for sprinkler systems sold for a few bucks at home cheapo). Then try to clean out the pipes going down and around the windows wells. Even though the drain tile is lightweight fragile pipe with no elbows to control a snake, you may want to talk to a plumber who has a snake and jet cutter to try to clean out the tile. It may break out of the tile and not go where it needs to but it may be worth the money to try it before bringing the backhoe and tearing up your yard. He could go in from the window wells and from the sump basin itself. A plumber with a camera would be a plus. If it worked, you could save a few years or so before the pipe filled up again.
Good luck. Post back with any more questions and the results of whatever you try. If it is more than a week, then start a new thread at the top.