Product: Credit card or prepaid card

This is for an XXXX store card through Synchrony Bank. I recently moved and applied for a new card to take advantage of the 5 percent off purchases. I was able to use the card online for about a week. The card was then turned off but the account remained open. I received a letter in the mail from the fraud department with a code from Synchrony saying to call them. I called them and went through a verification process and was told everything was fine. The card worked for 1 week then was not working anymore. 

I called back a second time and was told that no record of a previous call was on file. They attempted to verify and said my information on file is different and they will have to mail me a letter with a code to verify me. This letter never came so I called back. I verified my address and was told my current address is what they have on file. They said I just need to wait for the letter. Another week passes and still no letter so I call again. 

This time I spoke to XXXX who is the fraud manager. She verified my address and promised to send me a statement so I can see the charges to make a payment. I needed to make a payment and they would take money over the phone but refused to allow me to know what is on the account since they can not verify me. After going back and forth with XXXX I talked to a nice guy at customer service who did go over some charges and I made a payment so I do not incur late payment fees or interest. I then wait for the paperwork XXXX promised. 
About 2 weeks go by and I receive several letters in the mail that were forwarded from my old address to my new one. This old address was verified by Synchrony not to be on file and I was promised several times that items were mailed to my current address. I did receive a copy of a statement at this time. 
I called back to let them know I received the letters at the wrong address today. I spoke to XXXX who is another fraud manager id number XXXX and she did not care. She said she has to verify me or I can not even talk to them about anything. I told her that the information they have is wrong and the last 10 times someone has gone through the same script they said I can not be verified. I told her I wanted to close the account and given a final statement to pay the bill. She said she can not do that unless I mail them by postal mail a number of personal information items. I told her that I was just interested in closing the account again and she explained that if I do not send those items in then there is nothing she can do. I explained that they are required to at least provide a statement of charges so I can pay. She said that without that information they will not provide a statement, the amount due or any information on the account. I explained I can incur late charges if I miss the due date or amount due coming up soon. She said that information is only available once I go through the verification process. I explained how I went through it previously and she did not respond and just spoke the same statement. I really need help. These people do not care at all and might mess up my credit which has zero late payments and in good standing.