No Money back because of my signature

I went into the shop and asked for my money back as i had a lay buy with the store. The cashier asked me to sign and i signed, but my signature according to them was not the same. I then asked if my ID document does not count for anything and the cashier rep**** that it does not. I then asked her, what if i have to come and collect the lay buy and she said the same rule applies. I will not be able to get my lay buy or the money back.

I feel ********** as this is my own money that i am asking for as i do not want the items any longer.