Hyundai XG350 will not take gas

Sally, the problem is the charcoal vent system. A new one will cost about $150.00 but......... the total fix will require the cleaning of the vent valve on the gas tank. You will find small pieces of the charcoal (pellet size) in the valve. You must look close to see them. Think pencil lead size. Remove them and exercise the valve some. The valve is a push in and out type. I don't understand the reason the charcoal pellets make their way to the vent valve at the tank but they do because I found them in mine. They must travel out of the canister and up and over a dry loop in the vent line to get to the vent valve at the gas tank. This would take some vacuum to cause the pellets to travel. It also requires the poor construction of the factory instaledl canister vent outlet because there is a filter at the canister that is supposed to contain the pellets. This will verify you have gotten all the charcoal pellets out. The charcoal canister (located up under the fender is easy to replace). You can make a cheep fix by installing some scaring pad material in the vent connection line at the canister but that doesn't address the charcoal being plugged. This will keep the charcoal pellets in the canister.
You will have to drop the gas tank partially to remove and clean the vent valve. Keep in mind you are working on a gas system that is very dangerous. i.e. it doesn't like spark's. Only begin this job with a tank that is all but empty.
You can find diagrams of the vent system on the internet. So you can identify the parts I have referred to here.
I have done this work. It is not easy. It is an under the car and also through the car trunk operation. You will have to remove the gas pump via the trunk from the gas tank. Remember about the spark issue when you do this part of the job.
This problem is very common with Hyundai's and several other cars. It is because the manufacture has reduced the gas fill piping to roughly a 3/4" pipe and installed a government requied venting system that you have this problem. You will see that at the tank the opening is as fill lines used to be about 2" and at the gas nozzle area also about 2'" but the rest of the line is no larger in diameter than the gas pump nozzle. That is not to place the blame all on the car manufacture. You see it is always the government that is behind our frustrations in life. The EPA has told the car companies that the gas vapors we used to smell when the car was being fueled are no longer aloud. So the need for the charcoal vent system to capture the vapors of the gas as fueling is being done. Some car people have said that if you never overfill your tank these fueling problems never happen. i.e. the charcoal in the canister never gets wet with liquid gas only vapors. Note the warning stickers and owners manual cautions to stop the filling process when the gas nozzle clicks off the first time. Sally you will know if you have not followed this advise and fueled your car clicking the nozzle several times after the first nozzle stop. That is the way we used to fuel the cars in the good old days. However, I do almost all of the gassing of my car and I had the problem. So I say the car manufacture is responsible for the issue with poor designs in the system.
Lastly I can't stress enough the importance of not doing this job as a back yard mechanic operation because of the volatility of the gas. It can and will blow up if not handled correctly.
Good luck!!!!