Don't know how you have been let down in this manner. The Sale Of Goods Act strictly states that within the first year and in particular, within the first 6 months of owning a product that if any fault develops it is the responsibility of the seller who you purchased the item from to either replace or refund the goods purchased. In that six month time frame, the onus is on the seller to prove that the goods were fit for purpose. From what you have described, it is obviously not the case. After six months is when it gets more difficult to prove. You are well within your rights to demand a refund or replacement. You need to contact Amazon again as you purchased the item through their site. You, as a consumer, have rights!
There is a link in the 'Help' section for you to have an online chat with Amazon customer services. Quote the Sale of Goods Act and in particularly in regards to the six months aspect where the onus is on the seller when a fault has developed in the product within that time scale. 7 days doesn't cut it when you are dealing with a malfunctioning purchase. Really can't understand why Amazon has let the seller get away with this.