Aspire One 522 Won't Boot

My AO522 was working fine. I didn't use it for about a month and now it won't turn on or do anything. It is out of warranty - I took it back to the retailer. They told me the graphic card needs replacing, also the keyboard. A week later, they claimed the motherboard needs replacing. Then they said it can't be fixed and better to buy a new computer. The battery won't re-charge and nothing happens when I use just the AC cord. Until yesterday. I tried the power switch again and the four LEDS lit up, for about 10 seconds. The netbook has 2GB RAM and was running Windows 7 Ultimate (32 bit). [I know - a bit of over-kill for a netbook like this. But it was working fine for about 14 months.] I don't trust the retailer and am wondering what I can do next (if anything).